Not sure where your info on 320/321 operating the route via somewhere's from, flybmi.com details the route and aircraft!
• schedule (services operate via Riyadh)
depart Heathrow 11:30, arrive Dammam 22:35 (Mon, Weds, Sat)
depart Dammam 00:01, arrive Heathrow 05:55 (Tues, Thurs)
depart Dammam 00:50, arrive Heathrow 06:45 (Sun)
• the service will be operated by an Airbus A330, with 42 business seats and 156 economy seats.