Yes, everything's updated. I find it odd how it's just the ranged animations, other combat animations work perfectly, and the units being attacked just stand there, some disappearing after the attack's over if enough health's depleted, and not dying like they should. Archers also keep firing their bows, instead of just firing once or twice.
Perhaps an update I installed corrupted a file and made this happen? This never happened when I had Civ V without any expansions or updates...