If your save game files are from the original and you're running the Director's Cut version (or vice versa) it won't work. It may not work even if you are running save games from the same "version" - eg old original save games may not properly load in the current version of the original game (which is a separate download on GOG under the "extras" stuff on the right, where the manuals are).

Remember back in the day they shipped a certain version which was unlikely to be the actual current version because no digital downloads back then. So you would have to apply a patch later. And patches often broke save games.

So first make sure the save games are from the same version as you are trying to load them into.