Since DietPi is going for native X86 64 bit Steam or (parts of) SteamOS are maybe quite nice.
The GPU Drivers for Nvidia are implemented in DietPi already (with Vulkan)
http://steamcommunity.com/groups/steamuniverse/discussions/1/143387886726826685/
Links to the FAQ and repo:
http://steamcommunity.com/groups/steamuniverse/discussions/1/648814395741989999/
Also: Moonlight which is a streaming client for NVIDIA Gamestream
https://github.com/irtimmer/moonlight-embedded/wiki/Packages
@Invictaz
Had my eye on this aswell, want to test streaming 馃憤
https://wiki.debian.org/Steam#A64-bit_systems_.28amd64.29
Remove bundled libs:
rm -R "$HOME"/.steam/ubuntu12_32/steam-runtime/i386/usr/lib/i386-linux-gnu/alsa-lib
rm -R "$HOME"/.steam/ubuntu12_32/steam-runtime/amd64/usr/lib/x86_64-linux-gnu/alsa-lib
rm "$HOME"/.steam/ubuntu12_32/steam-runtime/i386/usr/lib/i386-linux-gnu/libasound.so.*
rm "$HOME"/.steam/ubuntu12_32/steam-runtime/amd64/usr/lib/x86_64-linux-gnu/libasound.so.*
Steam does not run after selecting from the start menu, alsno not when installing the Nvidia driver.
The packages you describe are still being installed, at least I saw them after selecting my ALC663 sound card...
Steam is unable to start since it cannot apply updates

I tried again. Dietpi is installed on a usb stick with 6gb free

Here is the bootstrap_log
bootstrap_log.txt
Partially it's permission issues. Partially related to driver and partially it misses pieces
https://wiki.archlinux.org/index.php/Steam/Troubleshooting#Steam_runtime_issues
https://askubuntu.com/questions/614422/problem-with-installing-steam-on-ubuntu-15-04
https://askubuntu.com/questions/771032/steam-not-opening-in-ubuntu-16-04-lts
https://bbs.archlinux.org/viewtopic.php?id=157825
https://bbs.archlinux.org/viewtopic.php?id=221007
https://github.com/voidlinux/void-packages/issues/4239
https://www.reddit.com/r/linuxquestions/comments/4o8xlc/ubuntu_1604_fatal_error_failure_to_load_steamuiso/
Maybe needs 32 bit Steam to run on 64?
Nudging to v155, clearly lots more work to do on this ticket.
@Fourdee I'm a little bit further now. Seems the coulnd't find bootstrap is because Steam is in the wrong place.
Dunno if that is fixable since it's now in Dietpi userdata folder
https://github.com/ValveSoftware/steam-for-linux/issues/4076
@Fourdee running the NVIDIA .run instead of the apt-get install needs the 32 bit compatibility files for Steam to work. There might be some Mesa conflicts I have seen. My latest error window is now somewhat like this. Some errors have been resolved, others not.

@Fourdee
I guess there is still work to do on this?
If it is not working reliably currently on we don't find the time to fix, we should properly disable it for now?
Time has passed and I made some update: https://github.com/MichaIng/DietPi/commit/93efa92a64a37ddbf2f1190d8d641f85d68998e0
We installed old/deprecated packages before, hence I updated our installer to pull the modern (and suggested/recommended by steam package) i386 Nvidia driver libs, if Nvidia driver is installed.
@Invictaz
The changed Steam data dir location should not be an issue since we symlink it from /root/.steam, hence the original path stays valid. However this does not work when executing the client as different non-root user. So I am thinking in this case whether the shared data dir is a good idea here, since it breaks the general multi-user functionality. Generally any user could be added to games, video (and on Buster render) groups and should then be able to run steam. There is not much integration like a systemd unit or such shipped with the package, which would execute as fixed user (like username = steam), e.g. autostarting on boot, and then reasonably use /mnt/dietpi_userdata/steam as data dir.
@MichaIng Great for picking this up again. I have the Nvidia driver running.
However, having the 32 bit Nvidia drivers is only part of the problem. AFAIK I did run the Steam client from both root and non-root user and it did not work. So what is wrong?
@Invictaz
The bootstrap bug should have been solved meanwhile btw. Also as said there has been some things changed about the Nvidia drivers/libs composition, hence I think this can all be best tested on a fresh DietPi/Debian Buster system.