You haven't missed anything. If you play fast and do not explore every area in the game thoroughly, you will end it fairly quick.
The game has more difficulties, but if you've done it on the highest one it does not mean you are over.
You can play 5 different classes, 6 with the expansion and for each class you can get different loot that affects your play style.
Diablo is RPG hack'n'slash game, repetitive at first glance, but the rewarding system (loot) is what keeps people playing. You are always striving towards better gear. :)
Either you love it or you hate it.