Board Game Arena

Hello, I have a question.

I've noticed after letting my premium account expire that I have trouble getting matched for games. Mainly, for Splendor. I usually don't even get matched, I have to quickly join an open table in the lobby to find a game. But here's my question: when I join a table, I usually get kicked out of the table. I will get a message that says, "BooglieWooglie quit the game" when I didn't. Then that table starts the game without me. Am I being bumped out of tables to let premium players get in? Is there a queue for non-premium players and I'm being kicked for cutting the line so to speak? Or is it something else?

Splendor is a premium game so it makes sense that you could find tables easier when you were a premium member. As a premium member you can play with the whole player base and now you can only play with premium players, so less chances of finding a match.
When it comes to you getting kicked from a table by the site my guess is, that the premium player left and therefore the whole table has been closed.
Since people can queue for several games at once it is normal that tables get abandoned regularly only now you actually notice it.

Premium players do not get special treatment when queuing for games and I am certain of that because that would be a huge selling point for premium memberships. It makes no sense to keep such a feature secret.

Correct. When there is no premium player in a premium game table before starting the game, the table is automatically cancelled.