Gut feeling is the red dot means "this queue is important right now/needs help or attention" yet it tells me the queue has been cleared. This is contrary to the grey circles, which go away after I have cleared a queue. What does the red dot mean? If it is to attract attention to a queue, why is the queue empty?
It means that the review queue indicator is broken and doesn't work very well.
In fairness, it used to be very broken (cf. this post in this meta and this one in the mother meta). That is, it used to display the total number of outstanding review tasks, regardless of whether you could review them or not; SE decided that displaying updated figures on how many review tasks are available for each individual user was infeasible for performance reasons.
This changed when they introduced the new top bar some four months ago, at which point we requested that they do away with that behaviour and it improved somewhat - or at least, the behaviour as programmed looks fairly reasonable, so long as the thresholds are set correctly. The behaviour you note (a red dot that indicates that there are outstanding reviews when the queue is in fact empty) is caused by caching at a finite frequency, and it is a false-positive that reflects thresholds which are ill-adjusted to the site's review patterns.
Unfortunately it appears that per-site manually-set thresholds are not currently being considered:
With 170 sites, it's not practical to ask each meta to give us their preference.
Instead, SE is currently looking into fixing criteria that will programmatically determine those thresholds from each site's traffic and review patterns. (More specifically, if I understand that thread and this one correctly, they're looking to make a second version of the indicator software that's even more trigger-happy than ours, and they're looking to set criteria that will enable the trigger-happy indicator for a given site.)
If you have opinions to voice on the subject (including, say, "false-positives are Bad Things and they should be avoided because they diminish or even eliminate the usefulness of the review indicator", in which case I wholeheartedly agree with you) then now might be a good time to voice them.
These questions and answers to both are on meta.stackoverflow.com:
What the red circle means tl;dr it is used to "direct folks to specific queues that need more attention - things like Suggested Edits or Low Quality."
Why the red circle shows when there is nothing to review tl;dr it's a bug/lag? Same issue reported at The Workplace Stack Exchange. It seems like each SE site has to have its thresholds tuned manually...