This can't be the COMPLETE code your using. Just quoting two lines isn't much help.
But I'll give it a shot...
Why are you setting the Extract options of AbUnzipper but are using another component for extracting??? (AbUnzipperTasks ??)
You need to set the ExtractOptions of the component you're using to extract.
Another problem. You're using FolderPath+'\*.*' as ExtractWildcard. Is the path FolderPath completely present in your zip? Normally you would just do '*.*' of 'folder\*.*' If FolderPath also contains a driveletter (i.e. 'C:\Folder\') and the zip does not... nothing will be extracted.
So:
AbUnZipperTasks.ExtractOptions:= [eoCreateDirs,eoRestorePath]; // <-- same component as for ExtractFiles !!
AbUnZipperTasks.ExtractFiles('\*.*');
Or
AbUnZipperTasks.ExtractOptions:= [eoCreateDirs,eoRestorePath];
AbUnZipperTasks.ExtractFiles(PathWithoutDrive+'\*.*');
(and make sure PathWithoutDrive only contains the relative path which is present in the zip)