You're also right, of course, that he's extreme right. So are other successful communists. Chavez was never anything but the leader of criminal gangs, as is Maduro. Khamenei in Iran is also extreme right of course, not even that different (his power also mostly comes from control over criminal gangs, and obviously the members of his gangs are about as muslim as bikini-clad pigs having a barbecue on a beach). There's other kinds, like UN's Guterrez or Jose Manuel Barosso, much less successful than Putin, but another violent enforcer of communism, now non-executive chairman of Goldman Sachs International. But again, is there even a single socialist in your entire country that can make a better claim to being a communist than him?
Makes you wonder how loyal current well known leftists are to leftism. Greta Thunberg, to stay on the Gaza issue, has made millions of dollars on her "green-left" activism. About 10 times the absolute maximum she could have earned as a politician (ie. 10 times what the prime minister of Sweden makes). And of course Nicolas Maduro is a billionaire. Putin, if you wanted to quantify it, can probably claim to be the world's first trillionnaire. So I'm going to go out on a limb here and say that they also have somewhat less complete faith in communism.