I’ve skimmed through the guys videos a few times, and although I don’t have any evidence for this, I believe the Mime Jr. didn’t evolve because either the evolution mechanism wasn’t coded into the demo, or this Mime Jr. in particular is evolve-locked.
Now, the second of the two is much more likely. Pokémon have been locked from evolving since Pokémon Yellow with the player’s Pikachu, and they’ve done it again with the Notch Eared Pichu and with Partner Pikachu/Eevee. It’s also possible they didn’t want this Mime Jr. to evolve during the demo. Reasons for this could be bugs with the demo or just not wanting to spoil the surprise.
The only way to test which of the two options is the correct one would be to play the demo and either catch and try to evolve another Mime Jr. If the second one evolves, congrats the gift Mime Jr. is evolve-locked! If not, it would be safe to assume the move-evolve mechanism for Mime Jr. didn’t exist in the demo.
Like the other answer said, Mime Jr. only needs to level up with Mimic. As we can see in the video, the player levels up Mime Jr. and the evolution wasn’t triggered.
Presuming this Mime Jr. can’t evolve, then deleting and relearning the move won’t do anything.
Hope this helps!