He is a hold-over from the Soviet-era, like Yuri Luzhkov. The major question, though, is how much power he actually has. For example, there is virtually no way that VVP could get rid of Yuri Luzhkov without some kind of backlash. Yuri's hold on Moscow is just too firm. And I feel as though that may be the case with Mintimer Shaimiev.
On the other hand, the Davos deal makes me think that Shaimiev is on his way out. And this article seems to reinforce my belief.