Well, I just tried Linux on the GPD Win.
Booting from a USB stick was painless (which was a bit of a surprise, as I expected UEFI to crap things out, but nope, no big deal!).
Of course, the screen was rotated on boot up
First I tried my ArchLinux install stick, as I love ArchLinux.
It had quite a few tracebacks in the boot up log and while the broadcom Wifi chipset was found, it couldn't connect to the access point (I remember that my sister-in-law has the same issue with a broadcom Wifi chipset... maybe the same. I never found a solution except for using a Wifi stick).
As I couldn't do much from here without Wifi, I tried a stock Ubuntu image.
The kernel is a bit older there, so at least the same or even more issues were to be expected.
The touchscreen works fine (except that you can't hit the tiny buttons with your fingers), the screen is rotated (as expected) and trying to rotate it crashes the unit right now - probably something with the Intel graphics driver (a more recent kernel might help here).
Wifi has the same issue, no soundcard was being found, no battery, brightness control or power management (still, running Linux kept the GPD Win a lot cooler than Windows), so yes - it's working, but missing A LOT of driver stuff.
I couldn't test 3D as Ubuntu didn't have the drivers installed and without Wifi... yeah
GPD might fix those issues (if they can, I don't think they can do much with the broadcom chipset, the firmware is closed), but who knows whether they plan to release a hacked up Linux install version or whether they will contribute to the kernel (if they're allowed to, if there's closed-sourced stuff in there...).
If they hack it up, it might be hard to install any other Linux distribution on there, and who knows whether you can update it or not...
Maybe these missing things will be fixed over time with new kernel versions, but maybe not.
Don't expect to run any stock Linux distribution without any issues from the beginning though!