I grew up i the 1990ies during the boom of the First Person Shooter games, or the FPS games as we may call them. Since then, most of the FPS games I played have followed me as good memories. And, yeah, I still play some of them today. The last few years, I have been an administrator of the Classic FPS fans group on Facebook. Reguarly, I've seen the question “Is this game title a classic FPS game?”. That made me think. Is there a clear definition? In one word: No.
A FPS game is a game where you shoot enemies or targets from a first person perspective. Well, that sound clear cut at first glance. But the genres of digital games have evolved. Sub-genres and hybrid genres have emerged, some of them with first person shooting in the mix. "Interstate 76", "Descent" and countless other games are in first person perspective, but is also based on a vehicle. You may say these games are in a sub-genre or a hybrid genre; FPS combined with racing or flight simulator.
Even if you exclude games like "Interstate 76" and "Descent", there are some gray areas genrewise. Some games are in a first person perspective, but they clearly have a focus on puzzle-solving or stealth with the alternative of shooting, like System Shock". They may be better suited in genres like role playing games (RPG), but you still have a first person perspective and you CAN shoot. That would technically make the game a FPS, even if RPG is a better suited genre. So, calling "Interstate 76" or "System shock" FPS games is not wrong, even if it's not the optimal choise. I still stand by the introductory definition for mentioned games, but with a note that they fit better in other genres.
The two most relevant definitions of “classic” are “of the highest quality and outstanding of its kind, judged over a period of time” and “a work of art of recognized and established value”. A definition worth noting is “very typical of its kind”. The definition of classic is not clear cut because we use the word slightly different. But time is a common factor in most definition.
Sale figures is also a popular factor to include. The 1980s and 1990s saw a rise in sales of personal computers for home use. The few FPS games published before the 1990s haven't got the sales figure or recognition as they deserve. But would low sale figures make games like "Maze war", "3D monster maze", "Wayout" and "MIDI maze" less classic? They were typical FPS games... so...?
iD software launched several FPS titles in the 1990ies, starting with "Catacomb 3D" in 1991. Their next game, "Wolfenstein 3D", turned the FPS genre into a mainstream genre. "Wolfenstein 3D"s graphics was based on raycasting, just like in "Wayout", eight years prior. But the selling point for "Wolfenstein 3D" were the shareware model; try a part of the game for free and buy the entire game if you like the game. "Doom" became even more popular with its support for network play and extreme graphics and violence. "Quake" added support for 3D and better support for network play. 3D realms' "Duke Nukem 3D" established itself during the same period.
The games from iD software and "Duke Nukem 3D" are considered to be good examples of classic FPS. They have age, recognition (both in press and in sale numbers), quality and they stood out from the crowd on release. They became so popular that their source code became the foundation for new and unrelated games.
Since the 1990s, we have seen games based on the same game engine as a prior game; "Hexen" and "Heretic" were based on the same engine as "Doom". "Shadow warrior" and "Blood" were based on the same engine as "Duke Nukem 3D". Some games became successes. Others are almost forgotten. Some games got a cult status because how bad they were. It tastes like irony to say a game is classic because it's worse than a train wreck.
After the new millennium started, many games have drowned in the marked. Some may say there are too few games of today that really stands out; the games look too alike. I wont poke that discussion with a ten foot shotgun, but I have a question; If all FPS games look the same, aren't they just "very typical of its age"? And if age is important to you; Why not use the definition "modern classics"?
Back to the question "What is a classic FPS game?" There are no clear cut answer. It's a question of definition. But there ARE some games that - without question - are classic FPS games, like "Wolfenstein 3D", "Doom" and "Duke Nukem 3D". Maybe we shouldn't call these games "classic FPS games", because they are LEGENDARY FPS games.