China has a single-party system, a politicized judiciary, and severe restraints on the media, all of which inevitably lead to rampant corruption. That said, it is fair to say that corruption in China may be endemic, but it is not the organizing principle of the political system, as it is in Russia, which has at least the illusion of a democratic process. Why is that?
I think there are two reasons:
1. The ownership of natural resources plays a far greater part in the Russian economy than in the Chinese: As a result, the Russian government gets to distribute wealth that is ultimately derived from oil like candy to its supporters. If Russia had entrepreneurs who created wealth without government help instead of oligarchs, the economic and political systems would be different, but no such luck.
2. The Communist Party plays a positive role in fighting corruption in China: While you may not agree with the CP’s stated ideology (I certainly don’t, and neither do many of its members), it on paper stands for something other than the accumulation of wealth by its members, and it uses its enforcement powers over officials who violate its standards. There is no similar mechanism in Russia; everything ultimately depends on the whim of Putin.