Hmm, are you scanning the QR Code on your device after the game over screen?
The QR code on itch just links to the main leaderboard page which won't have the "Enter Name" prompt.
(otherwise it could be a bug...)
Alright, after much digging I found a crazy bug and uploaded a new build to itch. It's still labeled as "Version 1.2" but if you download the zip and sideload it again, it should upload to your device.
You'll need to generate a new score though, the old links are "corrupted" in a weird way.
Thanks for reporting the issue, fingers crossed the new build will fix it! 🤞