Can someone explain to me how this can possibly be considered a draw?

IF you had 'completely obliterated the guy', the situation could not exist where he COULD move his King around, knowing a draw was likely as even with all your pieces left, you couldn't achieve 'mate'....!
Your opponent has no legal moves and is not in check. So how do you want to continue to the game. Have him move his king in check which is against the rules of chess?
When you are dominating like this just ensure that you don't put your opponent king in a stalemate.
Don't get angry at the site here, literally every normal chess site (and chess game) follows these rules.

Stalemate : if it's a players turn, he can't move any piece and it isn't check it's a draw.
Is this a popular rule? No. Does it make the game more fun? Debateable. Will complaining about it change it? Probably not.
As you can see I completely obliterated the guy and then he just moved his king around for ages to waste time. We both still had 3 minutes left so I wasn't worried about time running out but suddenly the game tells me its a draw? Wow good to know all I have to do is waste the other guys time with my king for as long as possible and I can salvage a loss.