Ran out of time but drew?

So if you're clearly winning and run out of time the game draws?
I'm thinking that shouldn't the game give the W to the opponent as he beat me well on time or does this rule apply irl too?

Edit: I played as black and was up 2 pawns in the endgame

From what I can tell reading your message, that game was drawn because White had insufficient material vs timeout. If White had enough material to actually win the game after a timeout, then yes, he would get the win. Otherwise, if one side times out and the other doesn't have the material to win (ie, single knight or bishop), then it's a draw. IRL, in tournament play, I think FIDE has rules around what is and isn't a draw, where a certain material advantage makes it a win, instead of a draw... but I'm not too clear on that.

There isn't a way to white to deliver checkmate even if you help him do it. So it's a draw. If he had at least a pawn, it'd be a win for white.