It would be good for you to provide a few more descriptions about the game - otherwise we're left to guess. A quick online search turned up the following
https://en.wikipedia.org/wiki/Linux_gaming
In particular
Quote:
1990-1998
The beginning of Linux as a gaming platform for commercial video games is widely credited to have begun in 1994 when Dave D. Taylor ported the game Doom to Linux, as well as many other systems, during his spare time.[2][3] From there he would also help found the development studio Crack dot Com, which released the video game Abuse, with the game's Linux port even being published by Linux vendor Red Hat.
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Could Abuse be the game your thinking of?