What would you describe them as?
Russia embraced capitalism heavily after the fall of the wall, even going so far as to invite American capitalist advisers and financiers over to help them convert the economy. The current system is more capitalist than socialist, though less lassez-faire than it was in the 90s. They do have a strong centralized government, I guess that's what you meant by federalist, but the practice of fleecing the oligarchs was more or less a political and economic move to stamp down the former communist officials who got rich off of privatization and pyramid schemes. There's other issues in governance of Russia as well, working as a mob state aligning themselves closely with Russian mafia groups, state terrorist policies against minorities, endless corruption scandals...
They might have what the West would regard as socialist
policies when they pay for someone's healthcare, but NOT a socialist government or economy. Putin likes the old guard because he's indoctrinated into it and benefited from it so he's down with the rhetoric, but they are away from a socialist economy/society.
Edit- Some political theorists actually think of Russia more as a Modern Mob State