I haven't seen the show but I'm just going to go out on a limb and guess that Christopher Tolkien had nothing to do with this show nor approved of it.
The Tolkien Estate approved of the project, that really is all that matters from a legal POV. I wouldn't concern ones self too much over who approved. Watch it, decide if you like it based on your own opinions. I don't think you will find much praise here though. We are probably a tough crowd.