But the government of Russia basically just acts like a big corrupt corporation, how is that really fundamentally different than what we deal with here?
Russia has a corrupt profit seeking government running the country
The US has corrupt profit seeking corporations running the country,
Again, tomato, tomatoe....
It's not as simple and direct comparison as it might seem
Most people in the West don't really understand the psychology of people in the East and they don't understand at all the nature of the change 20 years ago. Not their fault, but if you have been raised into believing free market democracy is the only way to go, then it is no surprise you are not able to understand how someone who has never lived in a democracy may think differently.
The first misconception is that the Change happened because the people demanded it. They didn't, it is not clear why exactly it happened, various versions circulate, it seems to have happened because the people on top allowed it to happen and even actively helped here and there, but it most definitely wasn't because the majority of people wanted to live in a democracy. To begin with, they had no idea what a democracy was, the only thing they knew was that people in the West had a better material standard of living (but they didn't know exactly how much better) and they wanted the same, but that was it. I am not from Russia so I can not exactly speak about the conditions there, I am from Bulgaria but that's in a way better because the curious peculiarity about Bulgaria was that the local leader Zhivkov happened to be prone to telling it exactly like it is without any sugarcoating which wasn't the case at all in Russia where everything was kept secret. A famous line of his was that "People understand freedom as having something to eat and drink" and it was a very accurate observation. People didn't want freedom in the way it is understood in the West because they never knew what freedom was and never saw any value in it. They had been transitioned directly from a traditional patriarchal, almost feudal society (it was a truly feudal one in the case of Russia only a few decades before the revolution and Bulgarians were officially semi-slaves in the Otoman Empire until about the same time) to a totalitarian system.
The second misconception is that a long and stable strong-man rule necessarily leads to more corruption. Yes, it does, relative to what you have in Switzerland. But it is paradoxically better than a nominal democracy with frequent change of administrations when the conditions for that kind of democracy do not exist. As is the case in Russia. The epitome of the totalitarian state was the Soviet Union under Stalin. And people will tell you a long list of very bad things that Stalin did, and justifiably so, however, corruption is not one of them. He is not known to have had billions in foreign bank accounts, luxurious yachts, harems of expensive prostitutes, and all of the rest that we usually associate with the archetypal dictator that lives on the back of the people. The reason is that those things weren't on his mind - if you look at what he did, even the very bad things, the pattern is consistent with someone who wants to stay in power at all costs, but whose policy decisions are made from a long-term statesmanship perspective, because he plans to stay in power forever. It was the same pattern with communists until the very last generation of leaders, the people who were in their 50s around 1989 - those older than them enjoyed a much better lifestyle than the average person, of course, but it wasn't anything excessive, and the reason is that they thought they were there forever and they had a mission so there was no reason to grab and steal as if there is no tomorrow. The bank accounts abroad only appeared towards the end with that younger generation that I mentioned, when it became clear that the system was going to fall apart soon.
Now once a nominal democracy was established, it was a completely different game - you were there for 4 years, if you lasted that long, so you tried to grab as much as you could so that you secure a good future for you, your family, relatives and friends, while politics, statesmanship, the long-term interests of the country be damned. It is a very destructive thing for the country if politicians behave this way. From the perspective of the people, and from a neutral historic perspective, it is much much better to have someone with all the power and operating under the assumption that he will be there for a long time so that this short-term "I'm gonna steal as much as I can now because I don't know if I am going to be in a position to do so tomorrow" behavior is at least to some extent restrained.
If you ask "Why is it that people elect such officials?", the answer goes back to what I said about some societies not being ready for democracy and being better off without it - you can not elect non-corrupt officials because there aren't any and people don't really expect that. In fact, the average person on the street who can invariably be heard loudly decrying the state of corruptness of whatever the current administration is would behave in exactly the same lawless manner if he were in a position of power. Which is true everywhere all over the world, the only differences are how much of a norm corruption is in a society and to what extent people have a long-term vision about things.
Given what it has done so far, it seems that Russia has a corrupt profit-seeking government that however also takes into account the long-term future of the country and that has put the mess that the country was in the 90s in some order. Which is an upgrade.
In contrast, in the US, you have elections, someone gets elected and gets a 4-year term in office. But in the second year there are elections for members of the Congress and then from the middle of the third year on, it is again campaign time for re-election. Basically, it is one continuous election cycle, with no stability whatsoever. From the perspective I outlined above, this is much worse than having Putin+Medvedev in office for 18 years