I'm not familiar with SteamOS and Valve hardware in general. Could I play something like Overwatch on this, and connect keyboard and mouse? Could I play other PC games like World of Warcraft?
It's just a Linux box, you can do anything that you can on any other Linux machine (including install Windows).
Linux more or less runs most Windows games. The ones that don't run are ones where the developer is going out of their way to make them not run - mostly with kernel-mode anti-cheats that just find themselves staring at the wrong kernel.
Steam makes that pretty seamless and Steam games "just work". For non-Steam games you need to do some tinkering, it's stuff that most people browsing this forum can do.
Note that the "just" is overlooking that it's more locked down than a typical Linux box, in that the OS filesystem is read-only and all app installs live in userland (though you can turn off the read-only behavior). For what it's worth I'm very much a fan of it as a default for a mass-market machine, but you'll run into weird gotchas if you want to do "programmer stuff" with it.
That's how a lot of modern Linux distros are because immensely better. Updates on an immutable OS are massively more reliable, it doesn't prompt you to merge diffs in config files, it never breaks, you never have to reinstall.
I've run Bazzite on my desktop for the last year and every update has just been hitting the "Apply" button in the settings page with my xbox controller. While on mutable distros it's always involved going in to the terminal and running a series of commands or opening the repo list and manually replacing the release name for Debian. I know there is a GUI software store to do it but it literally never works because some error will show up that isn't handled and you just get a generic error message.