Of course when races interbreed genes get shared and it can be difficult to tell which race a person has as ancestors just from physical characteristics since traits have different degrees of dominance. For example, in the top picture the girl definately has African ancestry even if its mixed with something else. The bottom picture is more difficult, but I would guess that there is some Arabic blood involved . There is room for confusion in both cases no doubte. But you could never confuse a pureblooded Japanese person with a pureblooded Spaniard.
Yes, the distribution of some alleles probably have a more scattered distribution than could be explained by geography and race, but it seems reasonable to me that some traits are unique to a particular race. Even more so, peoples of the same general race but inhabitants of different historical countries (i.e China, Japan) have distinctly different appearences. Why would that be if there was nothing unique about their genetic make-up?