The first question for you to ask is who is the other? If we identify the other as non-indian, non-tribal members, than there are a few encounters within the story. If you think of the other as simply different from you (or the main character) than there is a lot to look at in terms of the otherness that both men feel with each other and within the tribe.
Focusing on the obvious other of non-indian characters in the story, the first person who comes to mind is Cathy, the gymnast. The encounter with Cathy is brief, but informative. The three, Cathy, Thomas and Victor, exchange pleasantries and Cathy talks about her would be Olympic chance on the 1980 Olympic team that was faltered by the government boycott. This is a key moment in their interactions. After Cathy complains, Thomas remarks "Sounds like you all got a lot in common with Indians", and for the first time since the conversation began, no one laughs. Of course Thomas refers to the many years of the government refusing to recognize certain Indian rights, but this idea of the other being similar to Indians makes all parties uncomfortable. This is a good point for you to begin thinking about the idea of the other. Similarities with the other makes us feel uncomfortable. After all, there is a reason for the other being the other. What implications are made when we subjugate someone as the other? At the end of the flight and they part ways with Cathy, Thomas comments that she was nice, and Victor tellingly replies with "everybody talks to everybody on airplanes, ... It's too bad we can't always be that way". This gives further insight to how the men view the world, or otherness, around them. In certain situations we all get along, but normally we do not. What makes one situation different from another?
There are also several random mentioning of the other throughout the story. One that sticks out is the Fourth of July celebration. Thomas finds it amusing that Indians celebrate Independence Day, as he points out "It ain't like it was our independence everybody was fighting for". This comment changes the thinking of the story a bit. Who is the other? Are we referring to the other as opposed to Victor and Thomas? What Alexie stresses is that our main characters are the other. They are the other in this country and the other among their own people. Think about how the two characters are treated and perceived by the people on the reservation. The Tribal Council would not pay to have Victor's father brought back. You should ask why? Is it simply because of money, or is there an underlying cause? Perhaps it stems from the fact that Victor's father left.
The main point in all of this is think of the other in terms of Cathy and the other in terms of Victor and Thomas. How are people both the other and the non-other. I hope this helped.