Steam compatibility tools, such as Boxtron, need to install some files in users home directory. These aren’t deleted when software is uninstalled with the package manager. You can check the directory ~/.steam/root/compatibilitytools.d to verify.
There is Plasma Bigscreen that’s a modification for HTPCs. For touch screen based devices, a tiling WM is available for both Gnome and Plasma, though not baked in. IMHO bigger issue for both is a poorly working touch screen keyboard. This is something that SteamOS solves quite well.
Yes, just deleting Boxtron folder from compatibilitytools.d should do it. You can always play it safe and move it to another location, eg. ~/backup/. Uninstalling dosbox-staging shouldn’t be necessary.