We investigate the kinematics of neutral gas in the Small Magellanic Cloud (SMC) and test the hypothesis that it is rotating in a disk. To trace the 3D motions of the neutral gas distribution, we identify a sample of young, massive stars embedded within it. These are stars with radial velocity measurements from spectroscopic surveys and proper motion measurements from Gaia, whose radial velocities match with dominant HI components. We compare the observed radial and tangential velocities of these stars with predictions from the state-of-the-art rotating disk model based on high-resolution 21 cm observations of the SMC from the Australian Square Kilometer Array Pathfinder telescope. We find that the observed kinematics of gas-tracing stars are inconsistent with disk rotation. We conclude that the kinematics of gas in the SMC are more complex than can be inferred from the integrated radial velocity field. As a result of violent tidal interactions with the LMC, non-rotational motions are prevalent throughout the SMC, and it is likely composed of distinct sub-structures overlapping along the line of sight.