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.
Yes you can connect keyboard and mouse; Overwatch (https://www.protondb.com/app/2357570) and WoW (https://appdb.winehq.org/objectManager.php?sClass=version&iI...) should both work well, as do the vast majority of single-player games. Some multiplayer games with particularly invasive anti-cheat may not, so if you have anything else in mind best to check before buying.