Again, not something that grinds my gears, but in a way another entry in this "the genius of (some game franchise)" two-parter (the first one being about Pokémon games.)
I have previously written about id Software, and wondered what happened to them. They used to be pretty much at the top of the PC game developers (or at the very least, part of the top elite). Their games were extremely influential in PC gaming, especially the first-person shooter genre, and they were pretty much the company that made the genre what it is today. While perhaps not necessarily the first ones to invent all the ideas, they definitely invented a lot of them, and did it right, and their games are definitely the primary source from which other games of the genre got their major game mechanics. Most action-oriented (and even many non-action oriented) first-person shooter games today use most of the same basic gameplay designs that Doom and especially Quake invented, or at least helped popularize.
But what made them so special and influential? Let me discuss a few of these things.
We have to actually start from id Software's earlier game, Wolfenstein 3D. The progression is not complete without mentioning it. This game was still quite primitive in terms of the first-person shooter genre, both with severe technical limitations, as well as gameplay limitations, as the genre was still finding out what works and what doesn't. One of the things that Wolfenstein 3D started to do, is to make the first-person perspective game a fast-paced one.
There had been quite many games played from the first-person perspective before Wolfenstein 3D, but the vast majority (if not all) of them were very slow-paced and awkward, and pretty much none of them had the player actually aim by moving the camera (with some possible exceptions). There were already some car and flight simulators and such, but they were not shooters really. Even the airplane shooter genre played from the first-person perspective were usually a bit awkward and sluggish, and they usually lacked that immersion, that real sense of seeing the world from the first-person perspective. (In most cases this was, of course, caused by the technical limitations of the hardware of the time.)
Wolfenstein might not have been the first game that started the idea of a fast-paced shooter from the first-person perspective, where you aim by moving the camera, but it certainly was one of the most influential ones. Although not even nearly as influential as id Software's first huge hit, Doom.
Doom was even more fast-paced, had more and tougher enemies, and was even grittier. (It of course helped that game engine technology had advanced by that point to allow a much grittier environment, with a bit more realism). And gameplay in Doom was fast! It didn't shy away from having the playable character (ie. in practice the "camera") run at a superhuman speed. And it was really a shooter. Tons of enemies (especially with the hardest difficulty), and fast-paced shooting action.
Initially Doom was still experimenting with its control scheme. It may be hard to imagine it today, but originally Doom was controlled with the cursor keys, with the left and right cursors actually turning the camera, rather than strafing. There was, in fact, no strafe buttons at all. There was a button which, when pressed, allowed you to strafe by pressing the left and right cursor keys (ie. a kind of mode switch button), but it was really awkward to use. By this point there was still no concept of the nowadays ubiquitous WASD key scheme (with the A and D keys being for strafing left and right).
In fact, there was no mouse support at all at first. Even later when they added it, it was mostly relegated to a curiosity for most players. As hard as it might be to believe, the concept of actually using the mouse to control the camera had yet not been invented for first-person shooters. It was still thought that you would just use the cursor keys to move forward and back, and turn the camera left and right (ie. so-called "tank controls").
Of course since it was not possible to turn the camera up or down, the need for a mouse to control the camera was less.
Strafing in first-person shooters is nowadays an essential core mechanic, but not back in the initial years of Doom.
Quake was not only a huge step forward in terms of technology, but also in terms of gameplay and the control scheme. However, once again, as incredible as it might sound, the original Quake still was looking for that perfect control scheme that we take so much for granted today. If you were to play the original Quake, the control scheme would still be very awkward. But it was already getting there. (For example, now the mouse could be used by default to turn the camera, but only sideways. You had to press a button to have free look... which nowadays doesn't make much sense.) It wouldn't be until Quake 2 that we get pretty much the modern control scheme (even though with the original version of the game the default controls still were a bit awkward, but mostly configurable to a modern standard setup.)
Quake could, perhaps, be considered the first modern first-person shooter (other than for its awkward control scheme; which was fixed in later iterations, mods and ports). It was extremely fast-paced, with tons of enemies, tons of shooting, tons of explosions and tons of action. It also pretty much established the keyboard+mouse control scheme as the standard scheme for the genre. Technically it of course looks antiquated (after all, the original Quake wasn't even hardware-accelerated; everything was rendered using the CPU, which in that time meant the Pentium. The original one. The 60-MHz one.) However, the gameplay is very reminiscent of a modern FPS game.
Doom and especially Quake definitely helped define an entire (and huge) genre of PC games (a genre that has been so successful, that it has even become a staple of game consoles, even though you don't have a keyboard and mouse there.) They definitely did many things right, and have their important place in the history of video games.