When I create my ad, at the bottom I have been choosing "blank" for the "Link Target" section, but it is not opening a new tab on my website when clicked.
I checked your site source and "_blank" is being properly set as the target for the link. I also tested this functionality on other sites and it is working fine on those site.
It looks like you have a script running on your site from tunegenie.com that is intercepting the click. If you can, please try turning that script/functionality off and see if that fixes it. If it does, please contact TuneGenie support to see if they know why your target="_blank" ads don't open in a new tab as they should.