We study the kinematics of runaway stars using GAIA DR2 proper motions (PMs) of 304 field OB stars in the Small Magellanic Cloud (SMC) from the RIOTS4 survey. To identify runaways, we remove the SMC systemic motion from, and apply geometric corrections to, the PMs to obtain the residual peculiar velocities. We find that the SMC Wing has a systemic transverse velocity relative to the SMC Bar of (vα, vδ) = (62 ± 7, ‑18 ± 5) km/s. After removing this offset from our 68 Wing stars, we obtain 43 ± 6 km/s as the median total transverse velocity of all 304 stars. We find this implies that on the order of half of our massive field stars are runaways, as opposed to having formed in situ. We explore the two mechanisms that produce runaway stars: dynamical binary-binary interactions and supernova "slingshot" ejections. We confirm that both processes have a similar contribution to our runaway population, with the former inferred from the number of eclipsing binaries and double-lined spectroscopic binaries, and the latter inferred from the number of high-mass X-ray binaries. Moreover, our finding that the SMC Wing has a relative motion away from the Bar and toward the Large Magellanic Cloud supports models of a recent collision between the Clouds.