I'm not quite sure why this is, but when I try to review close votes, the only option I have is 'Skip.' A screenshot:
Is this because of my low rep?
So, there's a check that runs to see if you have access to the various options before giving them to you...
It checks if you have full editing rights before giving you the Edit button. You don't have full editing rights, so you didn't get the edit button.
It checks a whole bunch of privileges before giving you access to the Close and Leave Open buttons... It checks for the Close/Reopen privilege of course, but before it checks that it checks the Flag Posts privilege. And with 5 rep on a private beta site, you have the former but not the latter.
This is one of those weird things that only happens in private betas, because everywhere else you earn the ability to flag long before you get close and reopen votes. Arguably, flagging should be a 1-rep privilege here too, but... There's some really grim potential for abuse with that and so we cannot lower the rep-threshold for that privilege.
The proper fix here is probably to check the access review queues privilege before letting you into any review queue. Failing that, blocking access to the Close and Reopen queues until you have both Close/Reopen and Flag privileges would suffice.