Closing the question can be done only by users above a specific karma rating and not by everybody.
what are the requirement for closing a question
How many karmas?
then you should look at karma system
minimum reputation to close others question 3000 karma.
If you want to know more about karma system then this will help you https://blog.codechef.com/2014/11/18/the-new-karma-system/
you can refer to karma point system
Minimum reputation to close others posts : 3000
For more info about Karma System, see this: The new Karma system
If you come across any such thread, which you feel is a duplicate/related to on going contest or any wrong reason, report that thread.
You can mail the admins if you wish, they will see if any action can be taken.
I close the threads whenever i come across something breaking rules, or (in case i miss that thread) when someone mails me. Currently, as others said, privilege of closing thread etc. is available to high karma users only. Privilege of deleting answer or question is only with admins though (for now)