Yes, there really was a Quake arcade game, it wasn't just a PC game.
Released in 1998 by ID Software (working in conjunction with Lazer-Tron), Quake - Arcade Tournament Edition was a port of the original Quake for use on arcade machines.
What's it like?
These games were built in dedicated cabinets with Quake marquees and huge VGA open frame monitors (klov.com claims a standard resolution monitor, but I have played Quake on both monitor types, and looking at the screenshots, it is obvious that it is a VGA). These machines had no sideart to speak of, but the control panel and monitor bezel were also covered with familiar Quake graphics.
The control panel was laid out with a trackball on the right, with a firing button right where your thumb would be. On the left were buttons for each direction, plus change weapon, and jump. This layout feels almost exactly the same as a keyboard and trackball at home (but mouse users might need a bit of practice).
So, um what's the difference between this one and the home version?
The game was a little different from standard Quake. The game simulates a deathmatch round (with the addition of monsters), several cabinets can be linked together for group play. The levels available were not exactly the same as the ones on the Quake CDROM (most notably the famous Quake II map "The Edge" was in this game as well). Some monsters would drop prize packs when shot (this would dispense tickets out of the machine, as this was also a redemption machine). Finally, the weapon lineup was not exactly the same (more of a hybrid of the weapon selection from both Quake and Quake II).
What is inside the cabinet
Inside the cabinet was a standard AMD (or Intel as they weren't all the same) computer with a Quantum 3D video card. No JAMMA boards or anything like that at all. There was even a keyboard and mouse inside the cabinet. That would have made for the perfect general gaming machine (the machines could run more than just Quake, as they were normal computers).
I never saw one of these. I think you just made it up
There were only twenty of these machines ever produced. The game was in its final test phase (with machines on location in several places), when a contract programmer quit. No one ever finished the project. The ones that were made did not all survive, although some are still around. They would have been $7500 each, if they had even been released for wide consumption. So you may never see one of these, but you could certainly build a clone rather cheaply.
Fruan says he may have seen one of these in a New Zealand comic book store. I am guessing it was a knock off (as the source code to this game was leaked at some point), as it wouldn't be very hard to make one of these.
Chris-O says I think I saw something like this in the Arizona Mills mall, in the big game area who's name I can't quite remember at the moment
WickerNipple says I saw and played one of these in an arcade games expo in Nashville, TN... either the summer of 98 or 99, not sure which. no idea if it was "authentic" - but I remember being disappointed.
TheBooBooKitty says Any vague sightings could also be the "Sin" arcade game, which uses the same engine and has a similar cabinet.