Funny you should ask about that. I just dusted FF7 off and decided to play it again (never finished it the first time) a few days ago. So far, Ive only had one issue: The part when the party ends up in the "prison" and Cloud has to race in the Chocobo races to leave. For some reason, just before he actually races, the game develops an error and quits. What i did was copy the save file to floppy, install the game on my kids' Win98 PC, then use the save file to continue, and then saved it back to floppy, and back to my PC. Quite a pain!
But it does work for the most part. You may not have the same issue as I did, I'm not even sure what the error relates to. I know nothing about how FF8 works, but the demo does.