gtoal - Ryanair don't allow non-EU citizens to check in online. I suspect that if you had continued without ticking the box you would have been sent to the "buy airport check-in" screen, and you would have had to pay their check-in fee... probably for both of you if you are in the same booking.
I think that's what it is - I doubt they would restrict the whole offer to EU citizens.
What I would do (is the free flights offer still running?) is to make a booking for your wife first - then, once they have (hopefully!) accepted that make a separate booking for yourself.
Laplap - I am not complaining about the 4p, I am complaining about them advertising something as free when it isn't. "Free" is absolute. If they want to charge people 4p they should say so in their adverts. And you're right, 4p means there is a contract, 0p means there isn't.