Both Debian and Arch are very fine distributions. Your other three options aren't really good for what Valve is going for.

Gentoo is source based, and while distribution of binary packages is possible with it, why would they do that?

NixOs ignores FHS, and while it is possible to install a steam compatible runtime, why would they do that?

And Fedora belongs to RedHat, and why would they do that, when they actually try to switch away from a OS distribution controlled by one company?

I am not saying those distributions aren't good, just that it would not make sense for Valve to use any of those.

Debian (via Ubuntu) and Arch are probably the most well tested Linux distributions by gamers, that do not belong to a single company.

Gentoo, like Debian, has always been a good distribution for derivatives. It is quite flexible and you can definitely distribute binaries in the case of a commercial derivative. Gentoo has also been used more widely in the embedded world (because it has the ability to lower its footprint). Known derivatives include Chromium OS and CoreOS/Flatcar Linux. Both of them do not use the source model.

Fedora is also very friendly with derivatives and features the ability to upgrade painlessly through atomic upgrades/rollbacks, thanks to rpm-ostree. Something that is shared with Nix. RedHat is mostly a sponsor and Fedora is community-maintained. Unlike CentOS, RedHat didn't get any bad press on how it tries to influence Fedora. Fedora is pretty consistent and quite polished on the desktop side. You also get a distribution who has access to the most influential upstream distributors (including for the graphical stack for example).

Debian/Arch do not offer such things. Arch does not even offer a stable base to start from. Taking a random snapshot of a rolling distribution needs a lot of work. Ubuntu does that with Debian. All Arch derivatives are desktop distributions. It would be interesting to know why Steam did not continue with Debian. Is it bad experience on the previous SteamOS or inability for Debian to move forward?

I think you're overestimating how much Valve wanted to customize this. I'm pretty sure that a large part of the appeal here is that it's "just regular ol' Linux".

I expect the same. They probably will not provide much support for the operating system and just redirect users to the communities.

Yeah I love NixOS, but for something like this it'd probably be a mistake.

They'll surely host their own repository rather than use Arch's directly. There's no reason to question stability when they're in control of both ends, and Arch is light with excellent tooling.

It's a good fit.

I find that odd too, but in my recent experience, Manjaro has been the best Linux experience I've had since Ubuntu 14.04. Just install and everything works. Although Gnome was a bit of a hassle, xfce and Cinnamon run beautifully.