Probably possible through Apple Home Sharing. What type of computer? What OS version? If you add compatible media files to the iTunes application (PC or older Mac) (or to modern Mac Apple TV app or Mac Apple Music app, then the Apple TV box can access those media files through the Computers app. The Computers app on the Apple TV box will try to access a Library of media files on a local networked computer, on which Home Sharing service has been activated. The Computers app has tabs for movies, tv shows, music, home videos, photos, and audiobooks. When videos are not specifically tagged as e.g. movies or tv shows, then those video files will be considered home videos.
MP3 files are audio files (not video), and would be compatible.
MOV files can have various types of video (codecs) in it, so that may or may not be compatible. Incompatible files may need conversion before being shareable this way.
MOV files that have H.264 AVC video and AAC audio are compatible.
MOV files that have H.264 AVC video and AC-3 audio are compatible.
MOV files that have MPEG-4 Part 2 video might be compatible with the ‘legacy’ models Apple TV box (A1469 or earlier), but not with the modern models Apple TV box (A1625 or later).
MOV files that have different video and audio codecs are probably not compatible.
Video files benefit from being properly interleaved (short alternating segments of each stream, to make streaming easier with less in-file seeking) and optimized (metadata at the start of the file). That would be a task for the video encoder or a post-processing tool.
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support
Apple TV (3rd generation) [A1427 or A1469] technical specifications - Apple Support
I don't have an Apple TV account subscription and the media was never purchased via any streaming services
An Apple TV+ subscription or Apple media Store purchase or other commercial streaming service isn’t needed for the above.
An Apple Account is needed for using the Apple TV box, as well as for activating Home Sharing. The Apple Account for Home Sharing should match between the sharing library on the computer and the Home Sharing service on the Apple TV box.