Other sources such as Vegan Bite By Bite (page 210) make clear that the number "18" is the number of autopsy proven deaths from prostate cancer, not the total number.
The source of the "18" number is An Epidemiological Survey of Prostatic Cancer from the Annual of the Pathological Autopsy Cases in Japan The Tohoku Journal of Experimental Medicine Vol. 130 (1980) pages 159-164. This article explains that only 5,798 men were autopsied in 1958, so only a fraction of deaths were studied.
An updated report on the trends in cancer incidence and mortality in Japan, 1958–2013 Jpn. J. Clin. Oncol. (2015) volume 45, pages 390-401, illustrates in Fig. 2 that 2 per 100,000 men died of prostate cancer in Japan in 1958.
See also Comparison of Prostate Cancer Mortality in Five Countries: France, Italy, Japan, UK and USA from the WHO Mortality Database (1960–2000) Jpn. J. Clin. Oncol. volume 35 pages, 690-691. which shows that the prostate cancer age-standardised death rate in the USA was about 10 times that of Japan (not the ridiculously exaggerated ratio in the OP).
Also, Cancer Statistics in Japan (mentioned in a comment by pericles316) says, in the "1. mortality" data, on line 2339 of the "number" tab, that 431 men died of prostate cancer in 1958 and, in the "asr" tab, that this corresponds an age adjusted death rate of 2.1 per 100,000.