The thing you have to remember is not all hotels the contract with Design Hotels opt in to be affiliated with Marriott, around half of the Design Hotels do not. So even if a hotel property is booked through designhotels.com it has be also a Marriott Bonvoy reward affiliate.
Design Hotels Inc is really an independent hotel consulting service that offers a menu of service, affiliation with SPG and now Bonvoy is but one of options. They also produce a Hotel Design book yearly. Starwood bought a large percent of the company a few years ago but its still listed under own on the Munich stock exchange.