Russia’s quest for recognition has already suffered because of the refusal of Western leaders to attend the Games’ opening ceremony, even though China’s president, Xi Jinping, is going. The contrast with the high-level attendance at the Beijing Summer Olympics in 2008 is striking. Neither President Obama nor Vice President Joseph R. Biden Jr. will attend, a decision made after Russia granted asylum to Edward J. Snowden, the former National Security Agency contractor who leaked agency documents.