This looks like the kind of crop-and-paste job you'd see on the Photoshop Disasters site. In fact these dogs live in the Philippines, and were born without front legs.
Despite the fact that it looks like the poor guys would topple over the moment they tried to wag their tails, it is apparently possible for dogs to live normal lives this way, using their strong hind legs to perfectly straddle the line between cute and terrifying.