The difference is that a movie streaming app streams fixed content while game streaming essentially streams arbitrary apps, albeit limited to gaming in this situation. From Apple's perspective, this sort of precedent could lead to entire app ecosystems bypassing the app store via streaming. It would be a workaround to Apple's refusal to allow third party stores on iOS. The same risk doesn't apply to more constrained and static content like video, books, and music.

I feel its important to mention that the issue is not quite as clear cut as this, since we have interactive Netflix movies and an ecosystem of web-based apps via Safari, but this seems to be Apple's rationale.