For intercepting swarms of cheap drones? It's a great fit! Space-based lasers for intercepting ICBMs? Maybe? But true hypersonic weapons (which Kinzhal is not) fly only in air (after all, they use oxygen in it to fly), while being covered in a plasma shield which is really good at absorbing all kinds of electromagnetic radiation.
Meanwhile, with high enough laser power you get instabilities in air which act as a natural diverging lens for your beam, drastically reducing effective range of your system. Push power even further to compensate for it and you will get plasma, which does even better job at dispersing energy of your beam. So in the end, you get a very short range interception system with a minuscule time frame to perform interception of a hypersonic target.