Your answer demonstrates that you've thought about this problem, not that you've solved it. I like the idea of this app, but I would argue that the core promise of your app is technically infeasible.
EDIT: I clicked through to read your whitepaper and see that you've explicitly called this concern out and admitted the DRM scheme cannot be foolproof. That's admirable, and I'm glad you did address it. I would gently suggest you place that disclaimer somewhere in your FAQ as well.
There is, of course, no technological way to prevent someone from capturing a video through the analogue hole (i.e., pointing a camera to the video as it is played), even if we assume that is possible that a consumer device can be controlled to such an extent that its owner can't find a way to capture the video output digitally.
In my opinion this is fair, because the vast majority of bitter/petty ex's are not going to know how to, or bother with, reverse engineering an app to spite their significant other. They'd also have to do it when they're granted access to the app, which implies a certain forethought.
> How do I know my partner won't abuse my trust?
> You can't. However with Rumuki you have the discretion to only grant playbacks when you can keep an eye on them. You also have the option to revoke all playback grants and delete the recording if trust is ever lost.