They operated the route before Links Air took over.
No they didn't. Citywing aren't an airline so they haven't operated the route before. However both ticket sellers 'Manx2' and 'Citywing' have sold tickets on the route before with it being operated by van air europe, links air and flightline amongst others.
Personally I'd be very wary of booking with this seller as you could be palmed off onto any of their operators aircraft and you really don't know what you're going to get.