After playing a lot of Doom and build-engine games, I have come to this conclusion.

In Doom and W3D engine games, although the primary game is shooting and killing things, there's a surprising amount of puzzle work, it's not Sierra-level puzzling mind you but it's still there. You have to collect hidden keys/passcards to open selected doors, in additions there's many optional secrets with ammo, weapons and armor which can help get past harder parts of the game. Many of the late-game Doom levels have big labyrinth-like mazes which are no joke to try and navigate either.

Everyone thinks of Doom and "oldschool" build-engine games as nothing but mindless killing, but in comparison to modern shooters they were actually very thoughtful and complex in their level-design. The "puzzles" help to break up to the action parts and stop the game becoming repetitive.

Modern shooters have none of this, for the most part. There's rarely a locked door, and almost never item-based puzzles like having to find the key to a door. The level-design of modern shooters is linear and corridor-based, while build-engine maps were huge and tricky to master.

In my opinion, oldschool FPS were really adventure games, or en RPG's, because they took cues from the games of their era. Doom had the "head" of Doom guy just like an oldschool RPG had the portrait of your character, Doomguy also had no personality and it was made clear he was supposed to be "You", the player. In comparison modern shooters almost always force you to play an established character who isn't the player. Other build-engine games like Shadow Warrior, DN3D, Blood all had "RPG-style" HUD's showing health, armor and armor.

Here's a screenshot I took of SW when I reduced the screensize. It really looks nothing like the modern idea of what a FPS looks like. Look at the chunky UI, the Daggerfall-style sprite of the arms holding the sword. It looks like first-person RPG more than anything.

What you are describing has nothing to do with RPGs specifically, but western game design in general. Western games have always been more non-linear and rather "arena" based. In a Japanese space shooter you would be in a scrolling tunnel (think any Shmup) moving in one direction while in a western space shooter (lke Ateroids) you would be in a "bubble" fighting off the current wave.

The maze-like level design is basically an extension of that idea. Modern games ar linear because it's easier to script a story that way. The immersion of you being the hero instead of playign some given character used to be inherent to all games back at that time. As for secrets, well, any game had those; just think of Super mario Brothers with its secret blocks and warp zones.

As for the sprites and the interface, that was pusrely technical, it wasn't passible any oterh way. Finally, this is the real precursor to Wolfenstein 3D:
http://www.youtube.com/watch?v=VsTwTTwmCLw
Originally Wolfenstein 3D was supposed to be a stealth game as well, but id kept remvong parts that would break the game's speed until only the shooting was left.

I sort of agree with your assertion that the classic shooters aren't just mindless killing, although I wouldn't say they had the degree of puzzle solving that an adventure game did ( hybrids like System Shock excluded obviously). They could definitely be very complex, though. Duke Nukem 3D and Dark Forces had levels that were downright confusing at times (and had some puzzles to match the huge levels).

That's why I got confused when I played Painkiller- I fired it up and thought it was gonna be all Doom-like, but it turned out to just be rooms filled with boring, predictable waves of enemies. I don't remember Doom locking me in a room, forcing me to kill everything, and then making me repeat it for hours on end. Some of Romero and Petersen's map designs were downright devious.

Oldschool id FPS are first person derivatives of the earlier catacomb games. Those were overhead action games.

http://www.mobygames.com/game/catacomb

With more or less the same arguments you could claim that old FPS are platformer or specifically metroidvania offshoots, because they share similarities. I don't really see any closer links to RPGs and adventure games than to other genres. To me it seems rather the other way around, that the old FPS inspired RPGs and adventures to try and move into the 3D realm, but of course that's just another speculation.

That's why Doom 3 is more of a Doom game than Painkiller.

Even though you would think otherwise from the title.

Well, you would think otherwise from the popular reaction. I do believe that a lot of it was quite simply rose-tinted glasses at play - I'm not saying that those games were the same, god no, but Doom 3 was still, essentially, navigating trough a maze (altho simplified), looking for keys, and shooting monsters (less of them, yes, but more difficult individually.)

Doom 3 has some problems- but upon revisiting it this year, I've really warmed up to it. And we have to remember that most of the level design team of the original Doom had long since quit id. It was different from Doom I and II (and 64, which wasn't made by id but was surprisingly really good) , but it's a pretty good game overall. I don't think the id during the Doom 3 era had the same map making creativity, but at least they managed to keep it focused.

And hey, it was Adrian Carmack's last game to date. Since then I've pretty much considered id a tech house.

Yeah, but so's that game where you have to jam the square peg in the square hole.

I don't play it yet, but I plan to do :
Realms of the Haunting