Is President Obama successfully playing the games that Smith discusses in The Power Game?
In general, I would have to argue that President Obama has not successfully played these games. I would say that he has made serious mistakes in the agenda game and has simply been dealt a bad hand in the coalition game. However, his playing of the image game has in some ways been good.
I have discussed Obama's performance in the agenda game in my answer to your previous question so I will not recap it here.
As for the coalition game, Obama has tried very hard to build coalitions. He has talked about being post-partisan and has tried to work with people like John Boehner. The problem for the President is that this is not a political environment that is conducive to coalition-building. Obama has made some mistakes (as all presidents do), but it would have been very hard for him to build coalitions that included the Tea Party-influenced Republicans in the House no matter what. The Republicans are firmly dug in and do not believe it is in their interests to compromise, which makes coalition-building practically impossible. So, here, Obama has played a decent game, but has no results to show for it.
Finally, with respect to the image game, Obama must be doing relatively well. For all the problems the country has, Obama's own performance ratings are shockingly good. He seems to have managed to project an image that allows people to feel positive things about him even as unemployment remains high and recovery slow.
So, Obama has clearly not done well in the agenda game (his fault) and the coalition game (largely not his fault). This helps to explain why his reelection is in doubt. The fact that he still has a chance is due largely to him doing a decent job in the image game.