Well, I've tried to install an completely new installation of SW using Skidrow's Release.
and it turns out it works without any problems, well nothing like that happened of what you have described, kind of an silly question but I have to ask this:
Did the original game .exe work even before you installed the mod?, if it really did work before applying the mod's files, there must have been something something that corrupted the .7z archive while you were downloading, or some files just were wrongly installed, thats also an possibility.
Oh and make sure you run the newest installment of 7Zip, since the .7z file format can only be read perfectly by very few other Archivers, WinRar has the capabilities it seems, I don't know of any other tbh.
The last possible reason as of why it doesn't work could be just some missing DLL's, like not having DirectX 9 Jun2010 which sw3 seemingly uses, I don't say it needs to have this version, but its likely.
Eitherway, I hope you resolve this issue ^^.
PS: Heres the Magnet Link for the Release I've used.
MAGNET