Atomically thin two-dimensional (2D) magnets have given rise to emergent phenomena due to magnetic exchange and spin-orbit coupling showing great promise for realizing ultrathin device structures. In this paper, we critically examine the magnetic properties of 2D FeS2, a non van der Waals magnet, which has been recently claimed to exhibit room-temperature ferromagnetism in the (111) orientation. Our ab initio study based on collinear density functional theory has revealed the ground state as an antiferromagnetic one with an ordering temperature of around 100 K along with a signature of spin-phonon coupling, which may trigger a ferromagnetic coupling via strain. Moreover, our calculations based on spin spirals indicate the possibility of noncollinear magnetic structures, which is also supported by Monte Carlo simulations based on ab initio magnetic exchange parameters. This opens up an excellent possibility to manipulate magnetic structures by the application of directional strain.