  We use the kinematics of field OB stars to estimate the frequencies of
runaway stars generated by the dynamical ejection scenario (DES), the binary
supernova scenario (BSS), and the combined two-step mechanism. We update the
proper motions for field OB and OBe stars in the Small Magellanic Cloud (SMC)
using Gaia DR3. Our sample now contains 336 stars from the Runaways and
Isolated O-Type Star Spectroscopic Survey of the SMC (RIOTS4), and we update
our algorithm to calculate more accurate velocities compared to those obtained
previously from DR2. We find a decrease in median velocity from 39 to 29 km/s,
implying that the proper motions from our previous work were systematically
overestimated. We present the velocity distribution for OBe stars and
quantitatively compare it to those of non-compact binaries and high-mass X-ray
binaries. We confirm that OBe stars appear to be dominated by the BSS and are
likely post-SN binary systems, further supporting the mass-transfer model to
explain the origin of their emission-line disks. In contrast, normal OB stars
may show a bimodal velocity distribution, as may be expected from different
processes that occur with dynamical ejections. The kinematics of fast-rotating
OB stars are similar to those of normal OB stars rather than OBe stars,
suggesting that the origin of their high v_r*sin(i) is different from that of
OBe stars. We update our model parameters describing the kinematic origins of
the SMC field population, still confirming that for runaway stars, the DES
mechanism dominates, and two-step ejections seem comparable in frequency to
pure BSS ejections.
