The first track of the Fallout Tactics soundtrack seems to be corrupted. I have tried it on Media Player and RealPlayer, and both stop playing at 1:27 (out of 2:36). I downloaded the file again, but the new file had the same problem.

Not sure in your case but sometimes it can be a codec that is corrupted. That said, usually all files of the same media type are affected which does not seem to be your problem. So . . . it's probably a corrupted file in the download.
If no fixes are forthcoming from the community try VLC Media Player , my favorite, or Foobar2000 . Both are free,VLC plays everything I have flawlessly, Foobar2000 works well with all my audio but I use VLC for most everything.
If VLC or Foobar2000 plays the file than I would suspect Media Player needs some looking at, maybe a codec update? (Help, Check for player updates) I have never used RealPlayer so . . .
If you do install VLC, take the time to uncheck all the file associations except for the file type you are trying to play. The program, like Media Player, wants to associate all media files to itself . . . =)
Edit: Maybe the file has DRM in it . . .=)

Does the track sound like it's supposed to end at the point it does? Only some tracks I have seem to have their length miscalculated.

The track ends where it should - play it in a loop and you'll see. It looks like the file was badly ripped/extracted from the game and that's why the length is different. If it bugs you, you can repair it with MP3Val.

Thanks for this tip Thiev, I have not heard of MP3val . . . going to be a handy app for sure . . .=)

Post in the game's forums next time, please.

Thank you for the replies.
I can't install anything here at work, thanks to a combination of a few clueless colleagues and someone who installed Unreal Tournament on his work PC. It will be interesting to check my CD I made when I get home.
If the track is supposed to loop, it does so badly. Zur's tracks usually loop more smoothly. RealPlayer actually made a couple of sounds after the cutoff point. Media Player just skips to the next track at 1:27.

First fix the file - you should notice the difference. (or maybe my hearing sucks badly ;) - I think it loops well enough, but I'm using Songbird).