I have conducted a brief survey of Internet sources and cannot locate any definite discussion of a possible connection between the Chicxulub impact and the inception or acceleration of the Rio Grande Rift and the possibly related Laramide Orogeny.
I looked at the related post "can-impact-events-cause-widespread-volcanic-activity..." but do not see a specific connection (since that involved primarily the antipodal hypothesis connecting the Deccan Traps with the impact). I note that a 2015 paper, Triggering of the largest Deccan eruptions by the Chicxulub impact sets out a convincing argument that a pulse of mantle plume-head-derived magma fed the Wai Subgroup flows (in the Deccan Traps) and may have been triggered by dynamic stresses (Rayleigh waves) from the Chicxulub impact.
I read the Princeton University study Princeton model shows fallout of a giant meteorite strike that was given in one of the answers to the SE post referred to above. That study corrected some of the misconceptions regarding the proposed strength of antipodal accumulation of impact seismic waves, however, their animation showed the expanding concentric impact wave passing directly under the crust where the Laramide Orogeny uplift and the Rio Grande Rift spreading had either begun or began shortly thereafter.
The 2015 paper given above (Triggering....by Chicxulub) estimates generated seismic energy densities on the order of 0.1 - 1.0 J/$m^3$ throughout the upper 200 km of the mantle, sufficient to trigger volcanic eruptions worldwide based on historical examples. They go on to hypothesize that triggering of other events (like the Deccan Trap flows) might have been caused by transient increase in effective permeability of an existing deep magmatic system ("mantle plume head"). In fact, they refer to the Princeton model (Meschede et al 2011; link above) in estimating the 1000 - 3000 km (from epicenter of impact; 3200 km is the approximate distance to the Rio Grande Rift) energy density from Chicxulub at 0.1 - 1 J/$m^3$ (in their figure 4 in the 2015 paper already noted). This would be the energy density in the concentric wave (view the Princeton animation at the link given) passing directly under the Rio Grande Rift and Laramide Orogeny area (the latter the more easterly area under southern present day New Mexico, which was uplifted somewhat while the Rockies were raised).
It is already hypothesized that the Rio Grande Rift and Laramide Orogeny (the dating on those two processes are not well fixed, but seem to be near the end of the Cretaceous, i.e., around the time of the Chicxulub impact) likely involved existing pressures from the western subduction of the Kula and Farallon Plates already under the North American Plate as well as shallow oceanic crust subduction of the Pacific Plate. With the region inland already experiencing one or more magma plumes (the Socorro, New Mexico, region, i.e., Socorro-Magdalena caldera cluster of the central Rio Grande rift, hosts an inflating mid-crustal sill-like magma body at a depth of 19 km that is responsible for anomalously high earthquake activity in the vicinity continuing today, per Wikipedia), it seems very possible that the Chicxulub impact may have triggered or accelerated the Rio Grande Rift and also the uplift in the area due to the Laramide Orogeny uplift.