The AR-15 is the designation given to the civilian version of the M-16.
One of the defining factors of an assault weapon is the capacity for automatic fire (this means when you hold the trigger down, the weapon will continue to fire until it is out of ammunition or you release the trigger). As sold, the AR-15 is only capable of semi-automatic fire (this means the trigger must be pressed and released for each round fired), while the M-16 is capable of full automatic (and burst fire in later models, which fires 3 rounds for each trigger pull).
Thus, by definition the AR-15 is NOT an assault weapon, while the military version of the same weapon (the M-16) is an assault weapon.
This is an argument that does nothing but serve to derail the actual point. Anti-gun advocates like to use the term "assault weapon" because it sounds scary. Pro-gun advocates like to focus on their incorrect use of the term to argue against rather than the actual issue. It's an appeal to emotion vs an appeal to the dictionary, and accomplishes about as much as the athiest vs christian debates that are all over youtube.
Part of the problem here is that people are focusing on whether the rifle was an assault weapon or not, and it frankly doesn't matter. What matters is that this man was a crazy person who decided to do damage, and how many times he had to pull the trigger on whatever weapon he chose to use to do so is frankly academic. It would have been just as tragic if he had used pistols, and someone familiar with them could have done just as much harm just as quickly in a place like that.