If I'm inactive in the main menu of Jazz 2 for a little bit, the demo of gameplay from the second beach level autoplays. However, I can't exit that demo-playback and return to main menu by pressing the back-button on my Xbox gamepad, although it's no problem to exit the demo playback by pressing the Escape on the keyboard. I'm using the current build of JJ2+ (auto-updater updated to JJ2+ beta v6.2).

Thanks for the report! Just to make sure, does the back button on your controller work as Esc in other parts of the game?

Yes; the back button on my controller works perfectly as Esc in all the other parts of the game as far as I know. It's only the Demo playback that's affected as of my testing now.

New update: this also happens while viewing the High Scores entry in the main menu. The back button on the controller don't respond as Esc in the High Scores entry both in the main menu as well as when the High Scores are displayed instead of a Demo while idle in the main menu.