As stated in the readme file the OpenTitus team doesn't own the rights to the original game and its game files. OpenTitus is a standalone game engine that parses the level files, provided by the end user. The original Titus the Fox is owned by Titus Interactive, that went bankrupt some years ago, I'm not sure if anyone still owns the rights to that game.
I'm not sure if the correct name is "port", "remake" or "rewrite", it is a new game engine, written from scratch, that does the same thing as the original game engine, but is not limited to MS-DOS.