1) It seems weird to say that the model claims that there are a bunch of other models/events. It's saying that within some class, a certain result happens a certain fraction of the time, so it only relies on there being multiple events implicitly.
2) It doesn't seem necessary to claim that there are a "whole bunch" of other models/events -- there only have to be as many as the denominator of the probability stated as a reduced fraction, right?
3) I'm confused about the claim that there are other models. The rest of the text on the page seems to require that there is a class of events for the frequentist interpretation. If I flip a coin a bunch of times, under the frequentist interpretation, do I have a different model for each flip?