"Adaptation" might indeed be the wrong word. An adaptation implies a separate canon and often replacing the events of the source material. To put it another way, there are two ways to make a TV show movie: an actual adaptation and what I like to call a The Movie. Adaptations aren't very common and usually happen to shows that went off the air decades ago, in an attempt to cash in on nostalgia. Yogi Bear, that Beverly Hillbillies movie from the '80s, and The Last Airbender come to mind. I swear I didn't cherry-pick that list; I can't think of a single example of one that was genuinely good. A The Movie, meanwhile, is basically a very long episode of the series. Stuff like The Simpsons Movie, Serenity, or indeed South Park: Bigger, Longer and Uncut. They tend to work well because TV and movies are already the exact same medium, just with different formats and budgets.
Trying to make the video game equivalent of a The Movie is very difficult because you're actually working in a different medium now and have to work Video Game Mechanics? into an existing universe. You're liable to run into what I guess we could be very nerdy and call "meta-ludonarrative dissonance", where characters suddenly sprout abilities that they didn't have in the original series because a video game wouldn't work without them. You can still pull it off if your universe is sufficiently wacky already, or if the mechanics are still close enough to realism that you can shrug them off as abstractions of what's "really" happening. (Remember Yahtzee's idea about regenerating health indicating "luck" that keeps the enemy shots missing, action-movie style, as long as the hero doesn't stand in the line of fire for too long?) I think Batman: Arkham Asylum did that reasonably well, and that wasn't even connected to any particular Batman series.