I played it "back in the day" but I don't think I got very far. I was much more casual with games since I was like 20 years old and had lots of other stuff to do. I vaguely recall enemies that were like the Predator and shaman dudes, and some cool waterfall. I didn't remember how much story it had.

It's hard for me to really nail down exactly what kind of other elements I'm looking for though, as I don't think story is really the right word. Just... more context for your actions, maybe? I dunno. I'll still try Unreal.

Ultima Underworld was mentioned, there are games that were inspired by it.
One of them are early FROM Software games, before they jumped into Souls cart. I'm talking about King's Field series, Shadow Tower (2 games?) and Eternal Ring.
They have lot to explore, wander, mystery and iconic FROM feature - one big map with no loading screens.

Other games from different studios?
Frictional Games - Amnesia, Penumbra etc.
Neurohunter?
Deep Shadows games - Boiling Point, Xenus 2....
and Cryostasis on top.

From RPGs - wanted to recommend Might&Magic series but it have way too many fights, it puts Doom games to shame. So, Wizards&Warriors? You can set encounters ratio to lesser degree.

Why is that a shooter? (see thread title)
Same question...

Absolutely, Quake 2 is one of the most bland and boring things I ever played (Quake 1 was great, though). Everything is just brown, brown, and then some more brown. Unreal is much more varied and interesting, but I disagree about its length, as it is pretty long for a shooter, and in my opinion too long, especially as there are not a lot of different enemies, and you fight them over and over again.

I agree that some additional enemy variety would be nice. But I don't think the game is too long. Maybe the early game, which is somewhat more "maze shooter" than the rest of it feels a bit tedious. I feel like the game kinda "opens up" sometime after the water temple & arena, and only gets better and better as time goes. It's hard for me to have enough of it. Also I can't really find any other game that features a similar melancholic, otherworldly atmosphere.

My biggest gripe about Unreal is the gameplay. Simply put, I feel like I'm fighting arena bots. That is, they feel clunky and spongy and there's too few of them. As such, combat isn't very satisfying. But that's a common problem for that games from era.

To be fair, the enemy AI in Unreal was rather spectacular in 1998, especially compared to other shooters where they would just run towards you and wait to be shot. The Skaarj can jump, dodge, and more, wich was really impressive back then.

Depending on how much RPG is too much RPG, and granted that the game in question is focussed more on melee than ranged combat (although ranged elements are present), ShadowCaster might be worth looking into.

Aside from combat, there's exploration for items, an inventory system (with occasional use-item-at-spot-in-world interactions), shapeshifting for new abilities, and a reasonable amount of context to where you are and what you're doing.

To be fair, it's not a game without it's issues; still, I consider it somewhat of a flawed gem.

Another, more shooty possibility might be CyClones. It's very much a shooter (with some limited usage of inventory items), but there are some nice exploratory elements to it. Furthermore, the levels each involve some story-based mission and often actually resemble relevant locations--a facility may have offices; an alien spaceship may have engine compartments and a cockpit; and so on.

The controls can, however, be a bit of an issue at times. Still, it may well be worth giving it a shot! (So to speak.)

(Both of these, by the way, were made by Raven Software; once the masters of flawed gems, I feel.)

Looks like a mix of blobber and FPS. Interesting. Somehow I never heard of it before.

Sort of--it doesn't have the restricted movement of a blobber, if I'm understanding that term correctly.

It's based on a heavily-modified version of the Wolfenstein 3D engine, and thus in the manner of Wolfenstein 3D the player moves around pretty much freely, just in a world that happens to be constructed of right-angles.

That engine derivation, by the way, is a fact that continues to amaze me given that ShadowCaster includes such things as a sky, flight and swimming, and underwater sections accessible from a water surface.

It really is a neat game in many ways, I do think.