The only other possible contender would have been the OS ran by Tandy COCOs, but they were largely going downhill by 1988. Linux was first released in 1991 (per wikipedia).

Apple had a sales program called "Apple for Teachers", which was a discount program designed to get teachers to buy into the Apple/Mac ecosystem. They had a unique position over Microsoft in that they sold the hardware and operating system as a package (that only they could sell). There were several early manufacturers of PCs, including IBM, Zenith, Compaq, Dell, Gateway, and a myriad of private label store brands (they might not all have existed in 1988, but they were close).