Seems like your average raycasting. There is a reason for 20 tiles vision limit, probably. If you download and use Real Vision mode (which expands this limit to 100 tiles), you'll find it lags even on fairly modern computers let alone PCs of 90x.
The https://www.ufopaedia.org/index.php?title=Line_of_sight article points that some hacks were used, resulting in blind spots, circles being not-perfect and objects like UFOs having holes in them.
It's possible with raycasting. You either should increase resolution of raycasting (easier, laggier) or change raycasting in the way where such problem are not happening (extremely hard, lag-free).
What about X-Com Apocalypse? The realtime nature of the game requires fast FOV. But I guess machines running Apocalypse can precompute it. A few bytes per cell would be enough to cache visibility bitmap of nearby cells.
What do you mean by "precompute"? You mean that it's still done on the battlefield, or that the information is somehow stored in the game files (which would help explain the lack of random maps)? I guess the latter takes it a bit far though