The main page of the site has 5 main coverages. Right now, the fifth article is the Favourite Awards. I hope that helps.
Please let me know if you still face any problem with this.
Your link was fine for me Sabine http://www.atpworldtour.com/News/Tennis/2013/Moet-ATP-Awards/2013-ATP-Awards-Fan-Favourite-Voting.aspx
But ... I'd already tried it, chosen my singles player, doubles team, given my email, and submitted my vote. It said sorry, there was a problem counting my vote, and thanked me for my vote! It happened again. Third time the doubles teams had gone, just another list of singles players.
I'm fairly sure the same happened last year. I think I gave up trying!