Russia is desperate with its back against the wall. The invasion of Ukraine is a failure, with Russian troops stuck. The Kremlin is trying to boost its position by using one of its "super weapons". Russia may also have used it because Moscow is short on precision guided munition.
Russia has a clear technological advantage over NATO, as the Western Alliance cannot counter its hypersonic missiles. The use of the Kinzhal has unsettled the West and might reorient their approach toward Russia's operation in Ukraine.
Russia and NATO are developing a tacit set of rules and red lines to attempt to avoid a direct confrontation in Ukraine. However, tensions are high, and military wild cards bring a risk of miscalculation and escalation that neither side presumably wants.