Yes, it is an official product of CDSE which is a directorate of DSS which is under the "Office of the Secretary of Defense". See Department of Defense organizational chart.
There have been other similar products from various DoD organizations:
The above image was a US military product, published in Air Force 'Loose Tweets' slogan warns of social media dangers Stars and Stripes, 20 August 2015:
"Loose Tweets Destroy Fleets” — the Air Force’s twist on the famous World War II slogan, “Loose Lips Sink Ships” — is meant to remind servicemembers to guard what they share on social media, particularly given recent threats by Islamic State sympathizers.
U.S. Air Forces Central Command’s online message last week from Al Udeid Air Base, Qatar, included a photo of a fleet of F-16 fighter jets parked on a runway. It was accompanied by a story reminding airmen “there is sometimes a fine line between letting your friends see what you’re up to and providing an adversary critical information about your connection to the military and its mission.”
The AFCENT article speaks directly to the threat posed by Islamic State supporters, who on at least two occasions have acquired and posted online personal data of military personnel, urging followers to attack Americans in the States and overseas in retaliation for the air strikes.
As social media keeps evolving and there’s more and more avenues to let your friends and family know what you are up to, those same avenues can be used by ISIS sympathizers, ‘lone wolves’, to track down and hurt our military members outside the safety of the base,” AFCENT’s Force Protection chief, Capt. Jonathan McDonald, was quoted as saying. He used an acronym for the Islamic State.
Most recently, a group calling itself the “Islamic State hacking division,” posted the names and identifying information such as email addresses and phone numbers of some 1,400 former or current military and diplomatic personnel who worked in the United Kingdom, according to London’s Sunday Times. Most of them were Americans, though much of the information was believed to be outdated.
Air Force tips to post smartly include the use of appropriate privacy settings and checking with a supervisor before posting anything work-related; also encrypting email about work missions, using a secure phone line and shredding important documents.
The “loose tweets” catchphrase is not new, having been adopted earlier by the Navy and Army.
Before the carrier USS Theodore Roosevelt deployed earlier this year to support airstrike operations in Iraq and Syria, the ship reminded sailors on Facebook to “Remember: Loose Tweets Sink Fleets.” Sailors were told to be aware of what they’re posting, what hashtags they’re using and what security settings are enabled. The Army used the phrase even sooner. In December 2013, U.S. Central Command tweeted the same message, linking to a U.S. Army online story about social media usage titled: “Loose lips still sink ships, loose tweets sink fleets.”