The nearby, luminous infrared galaxy NGC 7469 hosts a Seyfert nucleus with a circumnuclear star-forming ring and is thus the ideal local laboratory for investigating the starburst-AGN (active galactic nucleus) connection in detail. We present integral-field observations of the central 1.3 kpc region in NGC 7469 obtained with the JWST Mid-InfraRed Instrument. Molecular and ionized gas distributions and kinematics at a resolution of ∼100 pc over the 4.9-7.6 μm region are examined to study the gas dynamics influenced by the central AGN. The low-ionization [Fe ii] λ5.34 μm and [Ar ii] λ6.99 μm lines are bright on the nucleus and in the starburst ring, as opposed to H2 S(5) λ6.91 μm, which is strongly peaked at the center and surrounding ISM. The high-ionization [Mg v] line is resolved and shows a broad, blueshifted component associated with the outflow. It has a nearly face-on geometry that is strongly peaked on the nucleus, where it reaches a maximum velocity of −650 km s−1, and extends about 400 pc to the east. Regions of enhanced velocity dispersion in H2 and [Fe ii] ∼ 180 pc from the AGN that also show high L(H2)/L(PAH) and L([Fe ii])/L(Pfα) ratios to the W and N of the nucleus pinpoint regions where the ionized outflow is depositing energy, via shocks, into the dense interstellar medium between the nucleus and the starburst ring. These resolved mid-infrared observations of the nuclear gas dynamics demonstrate the power of JWST and its high-sensitivity integral-field spectroscopic capability to resolve feedback processes around supermassive black holes in the dusty cores of nearby luminous infrared galaxies.