Mystified why game and scene views are so different

I followed this tutorial:

Great fun!

However, in my scene view it looks fine:

But the game view is completely different:

This is a default HDRP project with an HDR Skybox added and nothing else. Default Camera and Default Directional Light. I tried adding a single reflection probe. The default color space is Linear.

Any thoughts on how to begin troubleshooting this?

Did you checked which quality settings you use in your build?