Currently, it's impossible to know whether or not a new PictureGame is created, or if one is deleted (There's probably more actions in PictureGame, but these are the two that I can recall on the top of my head.) - the only way is to
keep manually checking Special:PictureGameHome, actually it looks like you have to bookmark it, Special:PictureGameHome doesn't seem to feature all of the games, only one of them. I created a PictureGame at http://social-tools.wmflabs.org/w/index.php?title=Special:PictureGameHome&picGameAction=startGame&id=3, but it doesn't appear at http://social-tools.wmflabs.org/wiki/Special:PictureGameHome. A feature like this would be quite useful :)
Edit: Plus another reason, QuizGame has a log at Special:Log/quiz (shows up as "Quiz question" log), so why not have one for PictureGame?