I used an ABTA travel agent and they booked me with a non-ABTA tour operator. Can they do this?

Yes. ABTA travel agents sell products from a wide range of suppliers, including non-ABTA companies.

ABTA's advice
Always read the terms and conditions of a company before making a booking. This will tell you if they operate your holiday or if they will be placing you in contract with someone else. If it’s the latter, they should tell you before confirming the booking what company your contract will be with.

See also the FAQ: What is the difference between a tour operator and a travel agent?