The ASVAB (AFQT) is not technically an IQ test.
IQ Tests, per se, are not issued to recruits for the armed forces. The U.S. Army does test people's capabilities, but not in a standardized IQ test (at least on the scale of the entire military recruit base) because they use a different testing method, the Armed Services Vocational Aptitude Battery (ASVAB). The ASVAB is also listed as the Armed Forces Qualification Test (AFQT). This test looks for different information than an IQ test does, though there are scores for generalized testing.
The areas that the ASVAB tests are:
General Science - measures knowledge of life science, earth and space science, and physical science
Arithmetic Reasoning - measures ability to solve basic arithmetic word problems
Word Knowledge - measures ability to understand the meaning of words through synonyms
Paragraph Comprehension - measures ability to obtain information from written material
Mathematics Knowledge - measures knowledge of mathematical concepts and applications
Electronics Information - measures knowledge of electrical current, circuits, devices and electronic systems
Auto and Shop Information - measures knowledge of automotive maintenance and repair, and wood and metal shop practices
Mechanical Comprehension - measures knowledge of the principles of mechanical devices, structural support and properties of materials
Assembling Objects - measures ability with spatial relationships
-"Understanding the ASVAB Test", U.S. Army
From this information, the test is scored in order to determine if someone is capable of joining at all, and what Military Occupational Specialties (MOS) they qualify for. The extrapolated scores are in the following areas:
Armed Forces Qualification Test (AFQT) - Paragraph Comprehension, Word Knowledge, Mathematics Knowledge, and Arithmetic Reasoning.
Clerical (CL) – Word Knowledge, Paragraph Comprehension, Arithmetic Reasoning and Mathematics Knowledge.
Combat (CO) - Word Knowledge, Paragraph Comprehension, Auto & Shop and Mechanical Comprehension.
Electronics (EL) – General Science, Arithmetic Reasoning, Mathematics Knowledge and Electronic Information.
Field Artillery (FA) - Arithmetic Reasoning, Mathematics Knowledge and Mechanical Comprehension.
General Maintenance (GM) – General Science, Auto & Shop, Mathematics Knowledge and Electronics Information.
General Technical (GT) - Word Knowledge, Paragraph Comprehension and Arithmetic Reasoning (AR).
Mechanical Maintenance (MM) – Auto & Shop, Mechanical Comprehension and Electronic Information.
Operators and Food (OF) - Word Knowledge, Paragraph Comprehension, Auto & Shop and Mechanical Comprehension.
Surveillance and Communications (SC) - Word Knowledge, Paragraph Comprehension, Arithmetic Reasoning, Auto & Shop and Mechanical Comprehension.
Skilled Technical (ST) - Word Knowledge, Paragraph Comprehension, General Science, Mechanical Comprehension and Mathematics Knowledge.
-"Understanding the ASVAB Test", U.S. Army
It should also be noted that although the General Technical "GT" score is used to determine whether certain programs are available to recruits, such as the "Green to Gold" program, it is not used specifically to determine who is able to become an officer. College is required for entry as an officer, and even the "Green to Gold" program is designed to help someone who has a desire, a minimum GT score, good recommendations, and is still young enough in order to obtain the college education required (Bachelor's Degree) to become an officer (through a contract). I was at the age that I would have been too old before getting through the program when I looked into it (about 27 or so, IIRC).
The AQFT scores are used to determine which fields within a branch of Armed Services you qualify for. High enough generalized scores such as the GT score will, however, provide the ability to join in a job that you are not technically qualified for according to sectionalized scores. (e.g. My Mechanical Maintenance score was relatively low compared to the rest of my scores, but my GT qualified me to learn any occupation I wanted to, so long as slots were available, including auto-mechanic.)
Most Army soldiers will know their GT score, and specific scores are required for certain levels of promotion. A soldier can opt to take the test later in order to improve their sectional scores, or may be required to take the ASVAB again if they have a break in service (as happened with me).
Rare racial backgrounds and the ASVAB
The ASVAB only tests those who are applying to try to join the United States armed forces, thus the number of people that are joining that would qualify as "Ashkenazi Jews," "Sub-Saharan Africans," "Pygmies," or "Australian Aborigines" would be too low to establish any form of baseline, especially since the only tracking data requested for racial demographics in the military, based on my personal experience of having taken it twice, are: White, Black, American Indian/Alaskan Native, Asian, Pacific-Islander/Native Hawaiian, Two or more, Unknown, and Hispanic (any race).
Enlistment into any branch of the U.S. military, by citizens of countries other than the United States is limited to those foreign nationals who are legally residing in the United States and possess a Bureau of Citizenship and Immigration Services Alien Registration Card (INS Form I-151/551 - commonly known as a "Green Card"). Applicants must be between 17 and 35; meet the mental, moral, and physical standards for enlistment; and must speak, read and write English fluently.
Emphasis mine. This does not allow foreign nationals to become commissioned officers or warrant officers.
Note that the ASVAB, the current standard of testing, was introduced the the U.S. Armed Services in 1968, though it didn't become standard use until 1972. From 1950 to 1972, the Armed Forces Qualification Test (AFQT) was used. It was intentionally used as a screening test. "History Of Military Testing"
The AFQT was criticized because it claimed to be used to determine a candidates ability to learn, but focused on testing what they had already learned instead, putting those living in poorer communities (and, thus, minorities) at a disadvantage, and studies by Herrnstein and Murray stated that there was no known way to significantly increase a national IQ average, even ignoring those contemporary studies that showed that educational intervention did so.
Stephen Molyneux and Racial Bias
It should be noted that Stephen Molyneux frequently tries to push a difference as being inherent based upon race because it fits his personal goals. Whether he is presenting it based on the personal decisions of people based upon race, or their genetics differences (or, more realistically, is being attributed to both factors by him), he is explaining the differences as being based on the status of being non-white/asian. He appears to explain differences based purely in an academic effort, but his cited research leaves much context out of the research (and appears to do so intentionally to show inferiority of others). This allows him to look like he is offering educated points that are heavily vested in research to the lay person that hasn't dug into these topics, and offers those with racial biases to quote him as an 'intellectual,' thus creating a Genetic Fallacy among those that quote him or his sources without doing further research into the studies.
Studies need to be controlled for economic status and similar impacts.
All of this said, it should be noted that many studies conducted on racial disparities in testing such as IQ do not properly address extenuating factors and control for things like economic background. It is a well established truth of our society that there are large disparities in socioeconomic status in our society split on racial lines. Since Caucasians tend live, on average, at a higher SES than most minorities (with the exception of Asian-Americans, based on median income), it makes sense that tests would show that Caucasians fare better on IQ tests. Unless the tests isolate their data to control for factors like this, the results may be true, but are highly unlikely representative of capacity for intellect at birth.
Socioeconomic status (SES) encompasses not just income but also educational attainment, financial security, and subjective perceptions of social status and social class. Socioeconomic status can encompass quality of life attributes as well as the opportunities and privileges afforded to people within society. Poverty, specifically, is not a single factor but rather is characterized by multiple physical and psychosocial stressors. Further, SES is a consistent and reliable predictor of a vast array of outcomes across the life span, including physical and psychological health. Thus, SES is relevant to all realms of behavioral and social science, including research, practice, education and advocacy.
-"Ethnic and Racial Minorities & Socioeconomic Status", American Psychological Association
The research isn't considered definitive on the impact of SES and education right now, but the correlation between the two is strong and consistent.
I can't validate the specific numbers you state, but they do fall, for the most part, in line with the divisions in standard Socioeconomic Status deviations based off of information like median income.
Race and Intelligence
The studies involved that generated your numbers were generated by IQ tests administered over the course of the 100 years, but the military didn't have anything to do with it (for the reasons above), and the results were analyzed in the 1990s not the modern day. These tests showed some interesting observations. These studies were collected by Richard Lynn and Tatu Vanhanen, creating averages for each of 113 nations and estimates of another 79 nations.
James Flynn and and Richard Nisbett's research showed that there were differences in IQ between races. Some people tried to interpret the differences between races in these tests as being genetically determined, but that during the initial time-frames examined, the IQ of all sectors of Americans studies went up close to proportionally, and African-Americans increased their IQ faster than European-Americans from 1945 to 1995. This indicated that, according to Flynn, increases in general education for all Americans, but particularly for African-Americans, had a very positive effect on IQ. This lends heavily toward nurture, not nature, being the cause for the discrepancies. It was also noted that the overall average IQ, regardless of race, raised far faster than could be attributed to genetic factors (evolution being a slow change over multiple generations).
A 2012 review of the literature found that the IQ gap had diminished by 0.33 standard deviations since first reported. This shows, even more, that it is likely level of available education that creates the difference, not any genetic racial bias. "Intelligence
New Findings and Theoretical Developments"
12 years U.S. Army Experience - including taking both written and computerized versions of the ASVAB