An assault rifle, by definition is a machine gun. The gun used at LAX wasn't (as best we can tell from the available information). So the first sentence in the summary is inaccurate.
There's speculation, based on a photo on Twitter that the rifle is a Ruger Mini-14, in which case it may not have qualified as an "assault weapon" as defined by Federal Law. Under Feinstein's last [failed] assault weapon ban, the Ruger Mini-14 with a collapsible stock was banned, but the other Mini-14's were ok. It would depend on whether or not the stock folds/collapses.
Under California law, the pistol grip, and ability to accept a detachable magazine are sufficient to classify it as an "assault weapon."
Looks like high capacity magazines were used, although they may have had inserts to render them legal (i.e. limit them to 10 rounds). If they are large capacity and he owned them before 2000, they're legal. Otherwise they would only be legal if they were limited to 10 rounds (or fewer).
We can say with high confidence that a semi-automatic rifle was used. Under the previous Federal assault weapon ban, and the more recent failed Federal effort, this rifle may or may not have been considered an "assault weapon." Under California law this rifle is an assault weapon. The magazines may or may not have been legal.