The doll was designed not to offend anyone, leading to this exchange:
2ND GIRL: She doesn't have a name.
ANNOUNCER: That's because last Christmas, we released a Native American doll named Flying Eagle, and we haven't heard the end of it.
The bit offered some good comments, but its intent was unclear. It wanted to satirize companies that make stereotypical toys, perhaps, but it seemed annoyed at the critics of such toys. The message seemed to be that "politically correctness" is neutering toys and making them no fun anymore.
Well, in the case of "Flying Eagle," the doll clearly was stereotypical. No modern Native woman dresses in buckskins or rides a horse to work. Nor does any modern Native woman have a funny Indian name like Flying Eagle.
A toy company should expect to be criticized for making such a doll. Clothing a Native like this is no different from putting a Latina in a poncho or an African in a grass skirt.
In short, I'd say the commercial was a nice try, but it failed to make its point. Or if its point was to carp about political correctness, it succeeded but its point was stupid.
For more on Saturday Night Live, see Indiana Jones in Saturday Night Live and "Navajo Girl" in Saturday Night Live.