  A tidal disruption event (TDE) involves the shredding of a star in the
proximity of a supermassive black hole (SMBH). The nearby ($\approx$230 Mpc)
relatively radio-quiet, thermal emission dominated source AT2019dsg is the
first TDE with a potential neutrino association. The origin of non-thermal
emission remains inconclusive; possibilities include a relativistic jet or a
sub-relativistic outflow. Distinguishing between them can address neutrino
production mechanisms. High-resolution very long baseline interferometry 5-GHz
observations provide a proper motion of 0.94 $\pm$ 0.65 mas yr$^{-1}$ ($3.2 \pm
2.2~c$; $1-\sigma$). Modelling the radio emission favors an origin from the
interaction between a decelerating outflow (velocity $\approx$ 0.1 $c$) and a
dense circum-nuclear medium. The transition of the synchrotron self-absorption
frequency through the observation band marks a peak flux density of 1.19 $\pm$
0.18 mJy at 152.8 $\pm$ 16.2 days. An equipartition analysis indicates an
emission region distance of $\geqslant$ 4.7 $\times$ 10$^{16}$ cm, magnetic
field strength $\geqslant$ 0.17 G, and number density $\geqslant$ 5.7 $\times$
10$^{3}$ cm$^{-3}$. The disruption involves a $\approx$ 2 $M_\odot$ star with a
penetration factor $\approx 1$ and a total energy output of $\leqslant$ 1.5
$\times$ 10$^{52}$ erg. The outflow is radiatively driven by accretion of
stellar debris onto the SMBH. Neutrino production is likely related to the
acceleration of protons to PeV energies and the availability of a suitable
cross-section at the outflow base. The present study thus helps exclude
jet-related origins for non-thermal emission and neutrino production, and
constrains non-jetted scenarios.
