A disclaimer for this game: I played it on a PC monitor via emulation, but the original cabinet's display had the graphics projected onto a curved mirror, to create the illusion that there was a 3D hologram in the middle of the cabinet. It doesn't affect how the game plays at all, but it's obvious that it's a game that was relying heavily on this for its appeal, so I thought I should mention it.
The game itself is a fighting game, though it's one that very short on features, even being released as early as 1992. There are four characters: Professor Chen (kung fu guy), Somchay Dompayagen (muay thai guy), Jack Garrison (big guy), and Dave (karate guy). There are no backgrounds, though the real cabinet had a few coloured blocks in it, to add to the futuristic semi-abstract hologram look. The four fighters also don't really have any personalities or backstories, nor is there any plot at all, or even any special moves. Just four guys punching and kicking each other in the void. Dave doesn't even get a last name!
So you pick a guy, you fight the other three guys, then you fight the world champion, who is you, but recoloured. If you beat the world champion, you get to fight in a little survival mode. There's no reward for any of this, though: like I said, there are no endings, and there's also no scores or time records. The controls are simple as you might expect: just the joystick and two buttons, for strong and weak attacks. It is pretty surprising that they went that way instead of a punch button and a kick button. Surprisingly forward thinking, considering how basic the rest of the game is.
Holosseum was apparently released as a conversion kit for Time Traveller, a laserdisc-based game that also used the curved mirror fake hologram display, after the laserdisc player in the cabinets starteed failing. With that in mind, it could be that the game's barebones nature was a result of having to get it out of the door as quickly as possible. But honestly, what I think is closer to the truth is that it wasn't made for fighting games fans, or even arcade game fans in general to be a game that they'd come back to regularly. I think the target audience would be families and other casual players who might be impressed by the visual gimmick, play one credit, and move on.
I think the game could even have been ported to the Mega Drive at the time, without losing anything except the hologram gimmick. But obviously they couldn't actually do that, because without the gimmick, the game doesn't really have anything else to offer, and if it could be played on your TV at home, the fancy expensive arcade cabinet would have lost all its prestige.