I'm going to say right off the bat that you will not be able to achieve the look they have with radio buttons with strictly CSS.
You could, however, stick to the list style in the example you posted and replace the anchors
with clickable spans
that would trigger a javascript event that would in turn save that rating to your database via ajax.
If you went that route you would probably also want to save a cookie to the users machine so that they could not submit over and over again to your database. That would prevent them from submitting more than once at least until they deleted their cookies.
But of course there are many ways to address this problem. This is just one of them. Hope that helps.