I'd say it's probably more of a mafia state actually because it's more organised. It became a mafia state. Towards the end of the Soviet Union and certainly after its break-up, it was a free-for-all. Democracy to some people meant freedom not to pay taxes, freedom just to go and take a factory if they had the right power, or got a piece of paper signed off, or had enough money to bribe someone. That's how the oligarchs rose up. It was chaotic then because there were so many state assets to be grabbed. Many of those state assets are now in the hands of Putin's inner circle.
So, it’s a mafia state. And I would say that Putin is Mafioso number one. And because it’s so entrenched it's very difficult to see that changing anytime soon.
And if the top is run by the Mafia then the Mafia has its tentacles everywhere. So in a sense, it's like a template fitting over the whole of the country. For example, there is no independent judiciary. Judges can be bought. And most Russians know that to get anywhere, you have to pay bribes. To get a seat in the Duma you have to bribe. Most Russians would say that everyone has their price. And if you're the one who's made the money, then you've got the brains and you'll have the thugs who are going to carry out your wishes.
"Towards the end of the Soviet Union and certainly after its break-up, it was a free-for-all"
It's slightly more sophisticated now than in the early 90s. At that time you’d hire people to set up a tiny kiosk to be open 24 hours or so to sleep inside it just to make sure that no one came down to threaten you. There’s less of that now, but that’s because things are much more organised from the top.
It may be rather more complicated than the categorical statements that mostly feed outside the country. Of course, a compromised system may be a sham, a fake, a facade masquerading for the real system. But it becomes a question of how much this sham could resembel an actual system: in this case, the state.
Russian state and state-related industry and infrastructure are humongous. And they function. They do so painfully ineffectively most of the time, with disregard for individuals, reputatability and decency, and with strange shadow systems interspersed throughout (majority of which are fueled by the regular, standard variety of nepotism and kickbacks, though).
But to simplify to the degree of declaring that Russia does not have a state system, and has instead some kind of shadow mafia state that substitutes for regular government and bureaucratic machinery, is misleading.
There is no mysterious shadow government working from behind the actual government. Instead, actual government is itself a clique or a set of cliques, bound by numerous unspoken agreements and clandestine business relationships... but still spending an inordinate, astronomical amount of money on creating at least a semblance, an appearance of a working social state. Precisely because it is both popular and allows to siphon funds towards personal welath much more safely and efficiently.
The subsets of government down the line work the same way: they take this trickle down money and spend it lavishly on appearances of development (or in some cases actual development), then pocket a percentage.
In a nutshell, they found out that creating an appearance of actually, fervently doing their job (just stealing at every turn and involving every tier of bureaucracy into their open secret) is the best form of control. A perfect crime. The more you spend on wildly popular projects, the more you can steal. The more inventive you are at adopting the most fashionable initiatives (electronic government, urban development, innovative education, nanotechnology, you name it), the more you can steal.
I think that when people say "Mafia state" they imagine a land of lawlessness, where the strong explicitly take from the weak, threatening violence and openly flaunting laws. This may be true for some countries.
But the current system in Russia is built on the notion of "stability". This means that most every stealing bastard here (except some old school fellas who were left over from the gang wars in provincial governments) steals under the auspices of patriotism, duty, and the greater good of the society. The success of such embezzlement is directly proportional to how lawful, patriotic, efficient, and modern they seem while they do it.
I often see comments by Westerners who joke about swift retribution from Putin for the smallest transgression in the form of a killing or jailing. In actuality, it's more subtle. Every jailing and murder is a showpiece, a signal; most other "inconvenient" people are just harrassed or "gray-listed" via legal or semi-legal means.
The aim here is not to instill a reign of terror, but to retain this mythical "stability" by making people unwilling to bother.
For example, the censorship that is rampant in modern Russian media, both state and privately owned, is almost invariably self-censorship, with only slight unofficial prods and briefings from FSB, FSO, or relevant ministries required to keep people on their toes. And the threats accompanying these prods are not so dramatic as shooting squads or GULAGs, but simply advising the registrar to recall their license, or saying a few words to their biggest client / advertiser, or drowning them in fines etc.