Your right. Putin sees geopolitics as a big ol chess game.
He even fooled Bush. Remember when baby Bush came back from Russia and claimed he'd looked into Putin's eyes and saw his soul.
Uh...yea, right. Bush saw exactly what Putin wanted him to see. Every since, Putin's squashing political decent, strengthening it's military and making plays reminiscent of the old Soviet Union.
GW Bush was far from a Reagan when it came to the Russians, but I think that episode had more to do with him just trying to put Putin on the spot. ie, "go ahead, prove I'm a liar".