Maybe it's because it was the first one I played, but something about the 2d aspect of this game gripped me. I don't have the same love for the games that came after it, the 3d graphics somehow take me out of the historical element.
The fact that in the older games you are basically playing on a map, gives off this almost board-game feeling that is cosy and immersive. (I know that civ was inspired by a board game)
Playing civ3 as a kid really made me feel like I was in whatever era I was playing at. Still remember those jazz fusion tracks especially.
Civ Revolution is not available for PC. So did you try a different Civ game on Linux? If you want play the PS3 version again and have a powerful machine, then emulating PS3 with RPCS3 is an option. The compatibility rating for the game on the emulator is rated as Playable.
EDIT: Oh you was talking about Civ3! Looks like I can't read, sorry. Well Looking at recent ProtonDB user reports, looks like Civ3 is playable on Linux. But its not perfect, reports say without music and you need to install C3X. I personally have no experience, so cannot assist further.