Ah, that sounds frustrating! Thanks for the detailed steps you took. The "Turn on Player2 AI" button should open up the Player2 website, so you can turn on the AI in-game without running their app. It's one of the only games in this contest that uses that new Player2 feature.
I just tested the process myself and it worked! I'll show you pictures.
Could you try again and see if clicking the "Turn on Player2 API" opens up the player2 website like you saw in the screenshots above?
I think you'll love the streaming vibes in this game, once you can play it!
PS: updated itch description to note that running the player2 app is no longer needed