Talk:Friends/@comment-68.133.32.139-20160211212530/@comment-25646419-20160213211327

Sorry for the delayed response! When each of your friends sign up, they must place your username in to be referred. Each of those friends must also make a purchase using real life currency. You do not need to purchase anything.

So the answer would be no - If you go to purchase the Steam version, you will not gain the skin. All of your achievements and customizations are shared between the browser version and the Steam version though for the record.