Except for the prize committees outsourcing roughly the same sets of judges, they work a lot like how you’d expect. The judges pickup a bunch of books and choose the ones they like the most. Since the author makes it clear how subjective the process truly is, you can assume that personal biases play a huge part in how winners are chosen.
Yes, as someone who has read the literature section of the (small) national newspaper with some regularity, this is pretty much all old news -- could glean most of this from reading for a year. You hear about the longlists and shortlists and panel of judges (after the winner(s) is chosen), and one would hope that at least the literary prizes are highly subjective.