In Japanese culure, the depth of one's bow is highly calculated and symbolic.
Obama is bowing to this imaginary "Emperor" as though he were a common Japanese citizen, or perhaps the garbage collector!
As an American President, a simple head nod would have been more than sufficient in the interest of politeness. The depth of this bow is absolutely demeaning to the The Office and our country.
Lest you think I'm exaggerating, note how other world leaders handled the same situation (H/T IMAO):