Keep in mind that the check mark is only for multi-player games.
Also, keep in mind that it isn't there to show who quits as much as it is there to show who completes rounds. Quitting or technical errors (regardless of who's end it is, WGT or your computer).
Start playing some blitz rounds, and play til the end, even if all other players quit, or have a "technical error" before the end. Much quicker way to complete many mult-player games.