Forgive the next question and I mean this in no way to seem offensive but you are sure that you have purchased the Wordpress version (30$) not the HTML version of this site (12$)?
Assuming this is correct then yes technically the "theme" or "Site" folder would definitely contain some PHP files.
I am not sure about defining names in stylesheets - I have never had to do this.
As standard once WP is installed on a domain then by adding the theme via FTP or admin should do it - the necessary style sheet etc. will be within that theme folder.
If you have installed the theme via FTP maybe try and do it via admin and see if that helps but if there are no PHP files etc in the site folder then it wont do much good.
To do this: Make sure the theme or site folder is a zip then in admin > Appearance > Themes ... select to upload a new theme and browse your computer to find the correct zip.
It does sound like perhaps you may have the HTML version of the site.