Updated as Of 2/28/13 @ 23:30 PST
*CONFIRMED* You have to at least get one word in for the match to count toward the 100 total. You can tell this by watching the counter on the main page where it says "Full games completed".
If you play a game without entering a word, the counter will not go up, so there has been an update assuring that you have to play at least one word for the match to count.
*UPDATE* Your Gamertag is linked over all games (i.e Web, Win 8, WP and IOS) so if you are playing on the XBox Live site and on your phone, it logs a TOTAL of all completed games. When I finished the 100th game (linked to my Gamertag across both the web version and the iOS version) i was on my phone. The achievement popped. I then logged onto the web version and played one more game and the achievement poppped. So 101 games total on the same gamertag to get the cheevo for both versions. Then play an additional game on each version to unlock across all platforms.