Playing this game will inevitably lead to many people randomly challenging you to games. You will find over time that a number of them did so just to get the Achievement for having 10 games active at the same time and have no intention of completing the match.
Scan through the "Their Turn" section to look for games that have been sitting idle for a week or longer. At this time, you can force an end to the game, and you will be awarded the (walkover) win regardless of the current score of the game. These wins count toward your win total for this Achievement. After forcing ten forfeitures, the Achievement will unlock.
has had issues getting the force-quit method to give him the 10 wins for this Achievement. Can anybody confirm that this method will still work? (Solution was posted nearly three years ago, and this may have been patched out.)