Is stealing an account in a game unlawful (haram), and what should I do with the stolen account if I am unable to return it to its owner?

What you did by hacking this person's account and taking possession of it is forbidden (haram), and you must repent to Allah Almighty and seek absolution from the account owner by returning it to him along with the value of your exploitation of it, unless he forgives you. If you cannot reach him, then give charity on his behalf equal to the value of the account and what you benefited from it.