Hey u/Deadeye117, you still interested in this shit? I know this is, like, 6 days too late but no one here really gave you the right answer and I've actually got it. Shit, I've even got proof.
First off, immersive sim's an incredibly shitty term. Just terrible. Doesn't explain anything at all. However it's old. Old as fuck. Probably older than you. It dates back to 1992 if not earlier. And the term makes sense, at least if you know the actual etymology. It's actually a combination of 2 different terms that both made sense in the 90s.
(Oh, before I go any further, you mentioned Bioshock. Bioshock's the weird one. It's kinda not an immersive sim, and it also is one... sorta... but also not. Y'know what I mean? More on that later. Just forget about Bioshock for now.)
Immersive Sim refers to the old Looking Glass Studios games from the 90s (Ultima Underworld, System Shock, Terra Nova, Thief: The Dark Project) as well as a small handful of games from the early 2000s (System Shock 2, Deus Ex, Arx Fatalis) that were created by ex-LGS devs after Looking Glass went bankrupt in 2000.
Looking Glass were this insanely influential, groundbreaking PC game dev from the 90s who made real-time 3D, first-person games at the exact same time Id were making the original first-person shooters (Wolfenstein 3D, Doom, Quake). In fact they actually beat Id to market, releasing Ultima Underworld 3 months before Wolfenstein 3D. And unlike Wolf 3D, or even the later Doom, Ultima Underworld was actually in 3D, so you could look up and down, jump, fly with magic, shit it even had physics... in 1992. And none of this was some 2.5D engine trick ala what you'd later see in Marathon or Duke Nukem 3D. You were looking up-and-down because the game was actually in 3D.
This is 'Why are immersive sims?' Think of it like 2 parallel lines of game development. Both studios were pioneering the real-time 3D, first person genre at the exact same time and while they shared some inspiration between the two of them, they were creating very, very different games. In the end Id won out and by about 2003-2004 the whole immersive sim thing had died out. And even though by that time Id were kinda a shadow of their former selves, other devs had picked up from where Id had left off. Almost all first-person, and indeed most 3D games on PC, built off of Id's model rather than Looking Glass's. For instance something like Half Life took FPS in a completely different direction but it's still built on Id's foundations rather than LGS's and the direction it took was almost the complete opposite to where Looking Glass had gone.
It's one of gaming's great 'what-if's?' What if Looking Glass's games had been more successful and Id's work had become the cult classics? What would gaming look like then? Possibly completely different, although there is a flaw in that line of thinking which I'll get to later.
Anyway, the genre's dead, or at least it was. As said before, it died around 2003-4ish around the time Invisible War and Deadly Shadows came out. It's made something of a comeback in the 2010s with games like Human Revolution, Dishonored and Prey 2017. However this is where the term gets a little funky and weird and stops making sense.
Well, shit. I haven't actually explained what Immersive Sim actually means, have I? Okay, it's actually a combination of 2 different terms, both created by Looking Glass to describe their games: Dungeon Simulation/Simulator and Immersive Reality, both of which date back to around 1992 and 1997 respectively. Dungeon Simulation's pretty easy to explain. It's literally a combination of Dungeon Crawler and Flight Simulator and it's what Looking Glass called Ultima Underworld when it first launched.
Ultima Underworld's one of the most influential games ever made. It's pretty much the first ever, real-time 3D, first-person RPG. And keep in mind it came out before Wolfenstein 3D, and was actually in 3D. It's more or less a feature-complete prototype of a modern first-person RPG even though it's only set in a single dungeon. Today we'd call it a first person RPG, but back then there already were first-person '3D' RPGs. Real time Dungeon Crawlers like Dungeon Master, Eye of the Beholder and even a few remaining turn-based ones like Wizardry 6 or 7. These games weren't actually 3D though, they were grid-based with 2D graphics drawn from a 3D perspective. These were insanely popular throughout the 80s, arguably starting with the original Wizardry in 1981.
Here's a quick comparison. Take a look at some footage of Eye of the Beholder. See how the 3D really isn't 3D at all? And keep in mind that game was the height of tech in 1991. Now compare that with Ultima Underworld from the next year and hopefully you can see the difference. And again keep in mind that Wolf 3D still hadn't come out yet and you couldn't even look up or down in that one.
The whole idea of Underworld was to take these grid-based dungeon crawler RPGs (Dungeon Master was specifically the one they were influenced by) and combine them with the 3D tech that had been pioneered over the last decade in space and flight sims (3D polygonal graphics, affine texture mapping, rudimentary Newtonian physics and so on.) Hence Dungeon Simulator, although at the time they called it a Dungeon Simulation since Microsoft had a habit of suing anyone who called their game a flight 'simulator' as they claimed it infringed on their copyright for Microsoft Flight Simulator.
And I've got proof. Here's an issue of an ancient, DOS era, online magazine from December 1992 with an interview with Looking Glass (Paul Neuarth and Doug Church) promoting the upcoming release of Ultima Underworld II (It's under Miscellaneous). If that doesn't work in your browser here's a text-only transcript. Here's a few choice quotes from Doug Church the lead programmer:
We started with the idea of a first- person dungeon simulation.
And here's a quote about their future games while also talking about the new CD technology and the infamous 640k barrier:
For now, CD and such will allow better cinematics, and more speech, but offer less than we might hope for the look of the next generation of flight simulators and other "reality" simulators.
Again, December 1992. That's how old this term is. If you look closely in the actual magazine you'll also find under 'Vendor Notes/Announcements' the first ever press release for Id's next game, Doom. A game which wouldn't come out for another 12 months.
Oh, and here's a few quotes from a later interview with Doug Church, from around 2004-5ish. On Underworld:
"I think for Underworld it was because we were doing a dungeon simulator and it was OK, well, we re going to take a flight simulator and put it in a dungeon. Hey, guess what, first-person."
"And then the next producer didn't really get it either. I think we were very lucky to find Warren [Spector] who was like My God, first-person 3D immersive play simulation indoors! This is totally new and amazing! Warren really believed in it."
And on Ultima Underworld's follow-up, System Shock:
"I think we saw that in Underworld, where we had this incredibly remedial physics but people still had fun throwing things and bouncing the superball around and trying to hit targets with things. And we said, Hey, let's do more of that because worlds have physics. On some level it's still just a dungeon simulator, and we're still just trying to evolve that idea. I really do think System Shock is just the somewhat obvious evolution of Underworld."
Told you I had actual proof. Anyway I've nearly run out of room. I'll go into detail as to what Immersive Reality means in the next part.