You can only delete games that have had very few moves played.
I don't think you can claim those games as wins.
BUT if you have a game where your opponent has run out of time AND it doesn't have a "Delete" link next to it in your "My Games" page, then you will see a little "Claim Win" link and a skull image next to it in your "My Games" page. Just click on "Claim Win", click "OK" on the confirmation popup, then start a new game.
If you don't see the "Claim Win" link, then either your opponent has not run out of time OR you need to wait just a little while for the system to update itself.