Atomic-scale disorder in two-dimensional transition metal dichalcogenides is often accompanied by local magnetic moments, which can conceivably induce long-range magnetic ordering into intrinsically non-magnetic materials. Here, we demonstrate the signature of long-range magnetic orderings in defective mono- and bi-layer semiconducting PtSe2 by performing magnetoresistance measurements under both lateral and vertical measurement configurations. As the material is thinned down from bi- to mono-layer thickness, we observe a ferromagnetic-to-antiferromagnetic crossover, a behavior which is opposite to the one observed in the prototypical 2D magnet CrI3. Our first-principles calculations, supported by aberration-corrected transmission electron microscopy imaging of point defects, associate this transition to the interplay between the defect-induced magnetism and the interlayer interactions in PtSe2. Furthermore, we show that graphene can be effectively used to probe the magnetization of adjacent semiconducting PtSe2. Our findings in an ultimately scaled monolayer system lay the foundation for atom-by-atom engineering of magnetism in otherwise non-magnetic 2D materials.