How is the Ryanair business model different from the F9, G4, or NK business model (which are all fairly successful here in the US)?
It's different from Spirit and Frontier in the fact that they fly from secondary airports and don't offer connections. They're strictly point-to-point.
In such they're most comparable to Allegiant, however they're going one step further than Allegiant. They're doing the things that Ryanair does, but Allegiant doesn't do. For example transfers to and from the airport. This is fairly common in Europe but new to America. No American airline does this so far, while in Europe Ryanair, Wizzair and several other airlines all sell transfers. A local subcontractor offers a shuttle service between the city and the airport and tickets are sold through the airline. That's one of the things why secondary airports are so successful in Europe. It's not public transport, it's an arranged shared ride.
Also look at the fares. In America the average fare difference between a ULCC and a legacy airline is about 20%. In Europe this can be up to 60% or higher. You won't find the ultra low Ryanair fares anywhere in America. If Americans have to pay 60 dollars for a ticket on an ULCC they call that cheap, if Europeans have to pay 60 euros for a ticket on an ULCC they'll most likely pass. Too expensive. Ryanair offers fares as low as 10 euros or sometimes even less. The euro and dollar are more or less worth the same, so you can compare them.
Moxy could perhaps bring those ultra low Ryanair fares to America. Of course only a few seats per flight, after that the price goes up. They make a loss on those seats, but it's good publicity. Their real earnings are in ancillary fees, which are more extensive than anywhere else. Rental cars, hotel rooms, it can all be booked through the airline. You don't just book a flight, you book everything else you need along with it. The flight is cheap, but all together it can be quite an amount of money.