After some promising posts on the internet about Linux compatibility of the GPDWin handheld, I took the risk and got one. And while it isn't perfect yet it does run pretty well :)

I got my GPDWin Rev.2 from here: https://www.dragonbox.de/en/571-gpd-win-rev-25-z8750-aluminium-lid-gpd-win-4260416651807.html

It is a small 5.5" clamshell Intel based handheld with a build in Xbox360 compatible gamepad and thus supports Steam games pretty well.
Due to the easy to use mouse emulator and the (not very good) full QWERTY keyboard other PC games can work as well.

It needs some tinkering to get Linux running on it (besides the preinstalled Windows10), but here you can see the current hardware compatibility: https://wiki.gnome.org/AdrienPlazas/GPDWin

Initially I tried installing Manjaro Linux (latest KDE release) due to the pretty detailed entry in the Arch wiki: https://wiki.archlinux.org/index.php/GPD_Win
It was running fine, but had some issues with the rotation of the touch screen and I never bothered compiling the currently needed patched kernel for it when I discovered someone did so already for Ubuntu.

So ultimately I went with Ubuntu GNOME 17.04, as GNOME works great with the build in touch-screen.

First you have to downgrade the BIOS, as Rev2 and newer don't allow vital settings needed for some hardware components to work under Linux. Get it here and install under windows: https://www.reddit.com/r/gpdwin/comments/5c9duk/gpd_win_general_faq/

Then reduce the Win10 partition with the disk manager (right click on windows start icon) to get sufficient space for the Linux install. 10GB at least, I went with 20GB but I am also planning to put most of my Steam games on an external 128GB SDCard.

Then create a bootable 64bit uefi Ubuntu GNOME image on a USB stick.

Before installing it helps to download a few files and note down some BIOS settings from here: http://hansdegoede.livejournal.com/17445.html

You definitely need that WiFi settings file, but just safe it somewhere on your Windows drive to access it from Ubuntu later.

You can also already download the kernel .debs that I found here: http://boards.dingoonity.org/gpd-windows-devices/linux-anyone/

Then plug in the Bootable USB drive and reboot while pressing ESC when starting to access the BIOS.

Change the BIOS settings mentioned above here and then save and exit. You can also probably directly exit through booting from the USB. It should give you an option for that as a one time boot on the exit screen it the USB drive was plugged in before entering the BIOS.

In the GRUB bootloader you can add the "fbcon=rotate:1" parameter for a rotated screen output and then install Ubuntu as usual for a dual boot uefi PC.

When finished reboot into Ubuntu. The login is rotated and I have not found a way to fix that, but inside GNOME you can use the accelerometer to rotate the screen and then lock the rotation (so far it forgets the rotation though on my system on a reboot... needs more tinkering I guess).

Inside gnome copy that .txt file in the firmware folder to fix the WiFi and after a reboot you can install the latest updates. Then install all those kernel .debs and edit the grub boot parameter as explained in the link above. Also apply that sound fix. I didn't have to do the step with the accelerometer etc.
Again after a reboot it mostly works.

I still needed to select the right audio output in the sound settings, and I have not yet managed to get Bluetooth working (seems though that it is possible to activate it somehow). But then you can proceed installing Steam and enjoy some fun games. It is surprising how well even relatively heavy 3D games run on it.