Is there a version of WWIII where nukes are not lobbed around the world? I don't think so. If that's right, then Gary is asking us to accelerate a timeline toward the end-game, mutually assured destruction and our modern world ending as we know it.
Mr. Kasparov implies that cratering the Russian economy with sanctions, isolating the country, ruining the lives of the Russian Oligarchs, are the actions of weakness. In my very western view, they are not.
If there is even a slim chance Mr. Kasparov is wrong and the non direct military pressures being exerted upon Russia will ultimately erode Putin's ability to exert authority on his slowly starving, battle weary, and drained military, then we have to do everything we can to increase that chance.
We need to take as many bullets out of the gun as we can before Putin pulls the trigger.
There isn't going to be a World War IV.