I don't really want to play devil's advocate when it comes to that putain de merde, but I'm not going to say he can't be autistic because he's Putin. It's always easy to accept some world-saving genius having autism, but if it's an evil prince of darkness, things get a bit tricky maybe.
I'm not saying he is autistic; I don't know the dude. Being a successful politician (bah) might be pointing to no, but consider this:
he rises up in a tightly regimented organization with strict rules on how to operate (I think some of us might like that, or even thrive in it), which happens to be the KGB, where he gets trained in observing people and interpreting their behaviours (which is what we try to do when wondering what an NT, or anyone else, means with this or that) and learns how to gain control of his own behaviour and how to act according to the situation.
Political behaviour is very premeditated. There's nothing spontaneous about it. It's tactics, it's playing a role, acting out a playbook. There is a possibility that if you put him in an everyday social situation, stripped from the aura of power, he might very well be just as socially inept as the best of us. (Not taking into account the wealth of information on human behaviour, including the behaviour of his political adversaries,he gained while in the KGB too, obviously.)
And it's not like I've never seen an aspie being completely enthralled by social conformity, holding on to it for dear life (because it's a graspable concept in a world of uncertainty) and going against anything that might challenge that concept...
Anyway, I don't know; just a quick thought experiment.