Since Ryanair's price guarantee probably only applies on routes it operates and since most other carriers don't operate on those routes I would imagine that Ryanair doesn't have to pay out very often, if ever.
This 'my airlines cheaper than your airline' really is nonsense. Most of the time people should say, "I shopped around and got the best deal on the day for the circumstances and I don't care who the flight's with.".
If the best deal is Aer Lingus then thats great.