Rating
Nobody has played it on Walnut yet, so it has no medal.
Installation
With the buttons above: Install, then Add game files... and pick your copy of Doom II: the disc in the drive, an ISO, BIN/CUE or MDF image, an installer or a folder. The game data is not part of the package, and Walnut does not offer it.
What works: DOOM2.WAD from Doom II 1.9 or the original 1.666: a CD, an installed copy, Steam's common/Doom 2 folder or the GOG installer.
More ways (a terminal, game-data-packager on any Debian system, copying the files by hand): Guides.
The game's home page: https://doomwiki.org/wiki/Doom_II. License: GPL-2.0-or-later engine, commercial game data.