There are a few games that had only a basic plot that was expanded upon in more detail by later games or movies. Doom for example.
It can be done. But all the examples I can name are in genres where narrative is a focus. I've got nothing like Angry Birds I can name.
If by "turned out well" you mean "turned a profit", probably quite a few.
If by "turned out well" you mean "created a film that was critically well-received or generally regarded as a timeless classic", probably not.