Well he didn't get it from the service (unless he stole it) - those weapons are held by the service and each airman/marine/sailor/soldier returns to the armory afterwards (i.e. deployment, patrol, assignment, etc.). Only in deployed environments and certain jobs (like CID and OSI) does the individual retain the weapon at all time. Security police return the weapon after a shift ends. It's about accountability and a few other reasons obviously.
However, as we saw in the video with the ambushing of one PO, the tactics employed were consistent of CQB (or CQC), in which any type of small arms can be lethal. As for sniper act, it's labeled that for the positioning from an undetected level (usually elevated) with targets in a kill zone. With the kill zone being a relatively small distance, an AR-15 or M-4 or just about any type of short carbine/rifle can be highly effective, especially with a scope and knowledge of adjusting sights and whatnot and the targets likely not wearing body armor. It's not like this guy was firing at targets 500-1000 yards away. I'd wager they were within 100 yards at most, and probably within 50 yards. A true sniper act would have been sitting a many yards away with a much different rifle, like Lee Harvey Oswald.