What appears in my MODS folder is a single file, labeled "d4e9a196-0cbf-447c-a4bb-825714849b2a-4.civ5mod". No folders or files are extracted from that.
There is a bug, I think, for mod installation when your games directory wasn't in C:. The bug resulted in the download occuring, but not being installed. I had a similar problem and the fix was to edit a config file, I think.
That "civ5mod" file is a 7-zip compressed file. You should be able to install 7-zip and extract that civ5mod file.