It seems like there is at least something behind the https://api.twitch.tv/kraken/game/ endpoint, since it is actually returning
{
“error”: “Not Found”,
“status”: 404,
“message”: “Game not found”
}
you might find something by experimenting, a simple id isnt enough apparently 
Also, i would support that endpoint, since it can be useful for statistic stuff (e.g. you want to track a single game)