  Direct-imaging exoplanet surveys have discovered a class of 5-20 \Mjup\space
substellar companions at separations >100 AU from their host stars, which
present a challenge to planet and star formation models. Detailed analysis of
the orbital architecture of these systems can provide constraints on possible
formation mechanisms, including the possibility they were dynamically ejected
onto a wide orbit. We present astrometry for the wide planetary-mass companion
GSC~6214-210\,b (240 AU; $\approx$14 \Mjup) obtained using NIRC2 with adaptive
optics at the Keck telescope over ten years. Our measurements achieved
astrometric uncertainties of $\approx$1 mas per epoch. We determined a relative
motion of $1.12 \pm 0.15$~mas~yr$^{-1}$ (0.61 $\pm$ 0.09 km s$^{-1}$), the
first detection of orbital motion for this companion. We compute the minimum
periastron for the companion due to our measured velocity vector, and derive
constraints on orbital parameters through our modified implementation of the
Orbits for the Impatient rejection sampling algorithm. We find that close
periastron orbits, which could indicate the companion was dynamically
scattered, are present in our posterior but have low likelihoods. For all
orbits in our posterior, we assess the detectability of close-in companions
that could have scattered GSC~6214-210\,b from a closer orbit, and find that
most potential scatterers would have been detected in previous imaging. We
conclude that formation at small orbital separation and subsequent dynamical
scattering through interaction with another potential close-in object is an
unlikely formation pathway for this companion. We also update stellar and
substellar properties for the system due to the new parallax from \textit{Gaia}
DR2.
