Beyond the differences in amount of detail being rigged, game characters usually have a limited set of motions. The character is going to walk, run slow, run fast, and change direction, for example. A film character has to move realistically, which means a much larger set of motions.
A film character might require several different rigs, one for each activity, each of which has a high amount of detail in the area of activity but maybe not anywhere else. Sitting and having a conversation would require a lot of facial rig detail, where a complicated fight sequence has to have good shoulder and hip detail but not so much in the lips and cheeks. A game character might need only one or maybe two rigs for all actions.
If you’re learned rigging for films, you’re in good shape to just dumb it down a little for games. It would be harder to go in the other direction.