Take the gameplay of a traditional roguelike. In particular, the game is turn-based with enemies moving only when you do, and you find treasures and level up.

Now, take away the randomness. The dungeon is now fixed. While we're at it, let's also take away item identification and permadeath, as those features don't work so well now that we have removed the randomness aspect. In exchange, we now have a nice hand-crafted dungeon.

How would you classify the resulting game?

A turn-based RPG?

I second this!

Fallout 1 and 2?

Not roguelike.

Isn't that Gorky 17 you are describing?

Yup, I'd say Turn based RPG as well. It might also be a turn based strategy game, though I see it less fitting with the dungeon exploring, leveling up, looting and single character. If you added puzzles to the rest, you could be talking about DROD RPG!
The absence of randomness and permadeath definitley kill the roguleike aspect, that's the only sure thing!
Now I'm curious: why did you ask the question?

DROD RPG (which I now own but haven't tried) actually made me think of this question.

I also like Shiren the Wanderer's puzzle mode.

(Of note, there's also Orcs and Elves, but that game is presented in first person (but turning takes no time) and that game doesn't have much in the way of puzzles.)

I remember a game that plays exactly like that. Forgot the title, is it tower of sorcerer or something
You gather item, get keys to open doors, and climb the tower. I never beat the game

[Edit]
found the game http://hp.vector.co.jp/authors/VA013374/game/egame0.html

"Not for Randalator"...?

DID SOMEBODY SAY...
https://lexop.files.wordpress.com/2015/04/tumblr_m4wsjxeobi1qe7736o1_500.gif
...PUZZLE?!!?!?!
The DROD series are officially puzzle games, but DROD RPG was changed slightly so RPG mechanics were included. Basically, it's a puzzle game with RPG elements.