Is putting a star contrast with close vote?
I am a little confused ...
The only star I am aware of if the one below the downvote arrow. This star is used to favorite a question. The linked question is currently a favorite of 3 people. You only need 97 more and then you will get a stellar question badge. Beyond a way to earn badges, favorites also show up in your profile. For example, you have marked 17 questions as your favorites: https://academia.stackexchange.com/users/41198/ssimon?tab=favorites so you seem to be familiar with the concept. There was a slight site redesign recently, so maybe the new look confused you.
The star has nothing to do with down votes or votes to close.