Good question.
I believe that Barry is now playing a very high stakes game of chicken.
If he knows (or strongly suspects) that Putin has incriminating and embarrassing information on him, then Obama has made a gamble. This being, 'I'll trash Putin and blame him for the WikiLeaks e-mail release, and then if he dares to release the info he has on me, I can say "SEE! I TOLD you he was a snake! And HE STOLE THE ELECTION FROM HILLARY! Trump is Illegitimate!"'
Bathhouse Barry is a coward, and you can sense that he fears both Putin AND Trump.
Putin can be a sort of a rouge, he can do basically whatever he wants, and US media and politics be damned. But Putin cannot prosecute Barry or go after his crimes.
Trump, on the other hand, can go after Soetoro Hussein's crimes (accepting illegal foreign donations, pay for play, money laundering, treason, vote fraud, racketeering, even murder).
If I were Putin, I would release part of the damaging info I suspect he has on Zero, and threaten to release all of it. Obama will either double down, or fold. Either way, Zero loses.
I guess trying to destroy Russia’s credibility against future disclosures would be the only potential benefit I can imagine for poking that bear. I think it’s a huge stretch to think that America and the rest of the world would buy it, but that may be the desperate ploy he’s trying.