Hmm. I don't have that. I just have the one folder inside the Painkiller folder labled "Savegames", with nothing inside it except the temp.000 file, which is 0 bytes. I've looked elsewhere, but this is the only place where the game is on my PC. C:\program files(x86)\GOG.com\painkiller black.
Now I've started a new game playing the second mission, and it's done the same thing at about an equivalent point into the game. It seems to accept only a certain amount of saves before it crashes and won't load anything. Since the game autosaves at checkpoints, this is a real killer. I think I'm going to ask for my money back on this one.
Looks like you are using Vista or Win7 as you have installed into Program Files (x86). Beware that this is a protected folder on these operating systems so some older games are unable to create saves within this folder (UAC and DEP acting to prevent alteration of the contents of protected folders after the software has been installed).
Because of the above you might find that your saves are being put into your User folder somewhere. Try looking in the below locations:
I always try to avoid this issue by installing into C:\Games\ though some newer games have it built into their code to use the User folder anyway.
Oh, as an additional note, you won't get your money back from GOG. Go read the terms and conditions that you agreed to in order to create an account with GOG. They provide the game DRM free, so even if they remove it from your account you may still have a copy on your hard drive, or in fact many copies, and so you cannot prove that you have removed all copies of it. Also, the save game issue is a known issue with the game, something that GOG cannot fix as it isn't due to compatibility and they don't have the source code to the games they sell, plus they are a distributor not a games developer.