Based solely on the videos, it looks like a walking simulator/adventure/puzzle game. I'm not seeing anything that seems to obviously require a VR headset. Can this game be successfully played on an ordinary desktop PC?

Yes, this can be played without a VR headset. The gamecard says it works just fine on a monitor, but I imagine you'll need to use a controller.

VR is just more cool and immersive. However, with most VR sets, you have to use a normal PC controller anyways, so it certainly is not necessary to enjoy the game. The option to play without VR is right in the startup in fact.