#43: God Save the Queen
To be fair, in your garden variety, run-of-the-mill monarchy, you don’t get to vote for whoever is at the top of the pile. Maybe you can vote for a local government, but it’s not unreasonable for people to think of countries with monarchies as not having the same sort of politics that, say, democracies do.
However, I’m going to guess from the context that this person is British. And given America’s close ties to the UK, it is a little bit silly for this person to be so completely unaware of British politics as to not realize that the existence of a constitutional monarchy means that people do have some say about who is at (or near) the top of the pile.