This “Putin sponsors terrorism” ad is real and is appearing now, probably in Russia, Ukraine, and eastern Europe. The question is, did the White House (or operatives working for it) place the ad or is it some sort of weird hoax to embarrass Obama? The wording of the ad makes little sense. Anyone with savvy would not create a Google ad where the meaning isn’t completely clear and obvious. Also, a Google ad can click through to anywhere and the person placing the ad does not have to prove ownership of the website.
All in all, this is quite curious indeed.