You're a genius! I don't know how you figured this out, but it's the only thing that got Wiz8 running for me (Win7 x64). Thank you so much! The only downside is that it won't launch from Galaxy. Minor quibble. The game runs fine directly from the .exe now, even without admin rights or compatibility mode.

To expand upon soosgjr's instructions:
Go to Run>regedit
Navigate to HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\GOG.com\Games\1207659230
Right-click "1207659230" folder and click "Export".
Name .reg file and save to any folder where you can find it easily.
Open newly created .reg file with notepad.
In registry, navigate to HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\GOG.com\.
Click Edit (upper left)>New>Key.
Name new key to "GOGWIZARDRY8"
For each of the values below "[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\GOG.com\Games\1207659230]" in your .reg file, right-click in registry>New>String Value, and input appropriate data for each line. (e.g. create String Value "buildId">R-click "build-Id">Modify>input "51402325434851029" or whatever your number is under "Value data:")
When all values have been added, run wiz8_fix.exe with admin rights. It should now detect the folder and say "Fixed!"
Launching Wiz8.exe should now work!

Nice, glad you got some use out of it. The Galaxy issue is a bit strange, I haven't been able to reproduce it on Win10 (and my Win7 box unfortunately has no networking), but also not surprising, as this patcher supposedly predates the release of Galaxy, so it might break something needed by it.

As for figuring out the problem, it's actually a pretty simple process. Microsoft has a utility called procmon, which lets you log the resources (filesystem, registry, etc.) used by your processes. Once you have it running, you just have to look for failed access attempts. Quite useful when debugging misbehaving patchers like this.

I followed the instructions you posted, and it worked! Wizardry 8 still doesn't work for me, unfortunately, but the solution you provided was able to make Wiz8_fix do its thing. Thank you for this.