Apple TV, 4th gen: Local storage of photos?
Nothing built into the system or available via the app store lets you have safe long-term purely local storage without a cloud backup.

Apps that pass the approval process have a few kinds of data, but for any significant data, they can be broken into two groups: data that's marked as "cached", and data that's marked as "backed by iCloud".

Both kinds of data can be deleted by the OS without any warning.

Data that's marked as "cached" is deleted when that happens. 
Data that's marked as "backed by iCloud" will be re-loaded from iCloud (possibly from a local caching server on your network if you have one) the next time you need it -- but also takes up part of your iCloud storage quota (even if you have a local caching server).

If you want to load content for offline usage, and you're not expecting to be able to play it back again a week later after doing other stuff on the device, then the "cache" type data is probably fine work for you.

Otherwise, you need to either store the data on a server somewhere (possibly as simple as a thumb drive plugged into an off-the-shelf router), or you need to sideload an app that breaks Apple's appstore rules.