Even idealist (folks who are actually inspired by ideas and ideals) have to make compromises when implementing their ideals in the real grubby world. Like at the turn of the Twentieth Century when the Suffragettes were gaining traction to get women the vote. In order to get the South onboard they had to throw Black women under the bus, to get Southern White women to support them.
Even if you credit Putin with actually having beliefs he would still be like most movers and shakers and would have to incorporate ideas of his enemies to survive. Lets assume that he is still a dedicated commie. He would still need the church and business capitalists on his side to stay in power in this new post Soviet world that he is in.
But I doubt that Putin is inspired by any ideals nor ideologies. He is just a gangster, but a gangster who has delusions of nationalist grandeur. So I think its naive to worry about which ideology he belongs to. He is just a dictator who wants to stay in power, wants to line his own pockets, BUT also wants power over more than his country. Would like power over a few neighbors (including former Soviet Republics).
Thats why I find the original post so silly.
Reminds me of what Al Capone once said: "I am not one them commie pinko radicals! I run my rackets on strictly AMERICAN lines. And theyre gonna STAY that way!".

As I understand it, many high ranking members of the Russian mob are former intelligence agents.