Yes, if you simplify things down to just combat, then yes, I kind of agree. But the thing that generally separates “RPG” from the rest is whether the player feels like they’re playing a role or just playing a game.
Akalabeth gives the player interactive choices (which weapon? Climb the ladder?). The limitations are a mixture of the platform at the time and the skill of the game dev (was built by a teen). But it’s obvious that player choice and interaction with the character was a major component here, and the goal is to get the player to the end.
Doom just presents enemies to kill. Yeah, you can change weapons, but it’s less in a “character choice” way and more of a “best tool for the job” way. Yeah, it has a character portrait, but I took that to be an indicator of how injured player is, not a RP mechanic. At no point do I consider the character, I just want you press forward to find the next area of monsters (monsters being the goal, not the end or whatever).
If we ignore “shooter” as a category, I think “first person action dungeon crawler” is a good description for Doom, and “first person dungeon crawler RPG” is better for Akalabeth.