Now regarding whether what you are doing is legal or not, I think it depends entirely of how you’re retrieving those URLs and if they can really be interpreted as being “public”. Are you “figuring out” the urls or are they simply there hidden in their front-end source?
In any case, he is the owner of the videos so he definitely has a legal ground to claim that what you’re doing goes against his copyrights, mostly because you’re facilitating some circumvention of whatever he has in place to keep them invisible to non-paid users.
I think what would be totally fair game is for you to put the source code in GitHub and let anyone run a version of your React App but INAL, so don’t take my word on it.
In any case, the owner should be more worried about to protecting his videos through a proper authentication system and not so much about the one guy who wrote a wrapper around his crappy website.
Just to be clear, I believe the owner is totally in his right to protect his creative work in any way he deems appropriate. I’m just baffled by the idea that his first instinct isn’t to fix the root cause of the issue.