The player losing comes from a resolving trigger, so both players losing at the same time from two different triggers cannot happen, because two triggers cannot resolve at thw same time. The trigers are put on the stack in APNAP order (Active Player Non-Active Player) and resolve in the reverse order. Since your opponent was the active player and you the non-active player, your trigger was put on the stack second and resolved first, making you lose the game. The game ended then and there with no chance for the other trigger to resolve and make the active player lose. So no, this is and should not be a draw.