Reinstall Galaxy client as admin to path X:\Games\GOG\Galaxy\ or ...\GOGGalaxy\. Set Galaxy exe in that folder runasadmin in compatibility.
Reinstall game to similar path X:\Games\GOGgames\. Set all game exe's runasadmin (optional if all can be executed from Galaxy client that already started as admin from game MORE section).

When reinstalling all that remove folders in Program Files and in Win user AppData\VirtualStore\. Make sure that win registry no have entries abot Galaxy client (not GOG in general) and about installed via Galaxy games (Mafia and if any other installed and uninstalled with client - all of them too). After downloading of each game you must check game files in Galaxy. better twice.
Mafia Configuration Tool must started as admin and make entries to both HKLM and HKCU sections of Windows REGEDIT.

Also:
http://www.pcgamingwiki.com/wiki/Mafia
But PCGW, same as any wiki, possibly not 100% accurate.

Here's 2k's official answer

https://support.2k.com/hc/en-us/articles/201332423-Init-Error-4215-or-4205-when-I-try-to-start-Mafia




Also (my 2 cents): For ANY game that was released around 2000, try to use dgVoodoo2. In these years DirectX and 3d pc game programming in general was a mess.

I install RU 1 DVD version and it work on Win 7 x64 and 416 nvidia driver like a charm. Also with ENB series.

I have no problems either, but there are people with Anti-Aliasing causing crashes and so on, for those a virtual 3D card usually solves the problem.