Yep. I have it running with an Intel integrated graphics chips. There was a driver I had to download direct from Intel instead of HP, though.

https://github.com/microsoft/wslg

https://learn.microsoft.com/en-us/windows/wsl/tutorials/gui-apps

https://devblogs.microsoft.com/commandline/the-windows-subsystem-for-linux-in-the-microsoft-store-is-now-generally-available-on-windows-10-and-11/