If you fly on QR from EDI to anywhere except DOH, you will be issued with more than one flight coupon, even though they might be printable on one piece of paper. You will change flight numbers (and probably aircraft) in DOH, and under the IATA definition you are therefore on a connection (or transfer) flight.
Under IATA's definition of direct, the only direct flight on QR from EDI is to DOH, and it also happens to be nonstop.
Direct flights can have one or more stops on them. For example SIA offers a direct flight from MAN to SIN which has one flight number SQ327 and is ticketed on one coupon. However it stops in Munich, and is therefore a one-stop direct flight. Similarly BA offers a direct flight from LHR to SYD, which stops in Singapore.