Firstly, I notice that the counts of messages lag by several minutes behind the current situation.
Secondly, the "Process" button is deliberately obtuse. It probably will work, but it won't say when.
Let's say that there are messages in the queue that failed to deliver, and are waiting a retry at some unspecified point in time. Due to point (1), I can't tell if they're really there or not. If I believe that they should be delivered, select the queue in question and click Process, then due to (2) I have no idea when exactly it's going to try delivering them.
So maybe they've tried to redeliver and failed again (you can't read off the next retry time or last delivery attempt time), or maybe they've not yet retried (it's still thinking about it), or maybe they've all been delivered but still show up in the message count as it's not noticed yet.
The Process button should apply immediately and make this clear, and refreshing the queue summary should read off up-to-date figures instead of figures from ten minutes ago. It's really awkward having a UI where you have no idea if it's telling the truth.