If you want to be really in depth with it, the M-16 doesn't really exist in the way it does in the real world because it was made during the end of the 50s, just after the real universe and the Fallout universe split, and was issued even later than that (obviously). Could be the same for most IRL weapons, though it would depend when they were made and issued. Could explain why there's not as many modern guns like the M-16, but there's other, older real weapons like the M1911. That's what I always thought, anyway
EDIT: Just checked, and the RPG-7 was in fact made right at the beginning of the 60s, so that would explain why it's not there. The AK-47 however was made right before the 50s, so I can't figure that one out
Just because there was a timeline split doesn't mean that no weapons post-atomic age weren't developed.
http://fallout.wikia.com/wiki/Desert_Eagle_.44_(Fallout)
http://en.wikipedia.org/wiki/Desert_Eagle
The Desert Eagle was originally designed by Bernard C. White of Magnum Research, who filed a US patent application for a mechanism for a gas-actuated pistol in January 1983. This established the basic layout of the Desert Eagle. The Desert Eagle was originally designed as a revolver, but was later reshaped into a semi-automatic pistol. A second patent application was filed in December 1985, after the basic design had been refined by IMI for production, and this is the form that went into production.
There were plenty of post atom-age weapons in Fallout, Fallout 2, and Fallout Tactics. M16s, Pancor Jackhammers, MP9s, etc.