So, the permission here really lies with the original creator Freya (communistsister on itch). However, tweaks to any version of Videotome are fine for any game you make with the engine. It's good practice to mention any tweaks made on you game page, just to help curb any "I saw [x] done in [y]'s game, how do I do that?" comments me or Freya might get.
If you'd like to publish just the engine with your tweaks as a fork, with the intent for other devs to make their own stuff with that fork, you'll need to speak to Freya as I can't extend permission on her behalf.