To be fair and make a point, that was the reason Kyle, and most other Americans joined and went over there (Not going to discuss those choices, but its the reason). That scene had a couple of effects. It related to the military community because seriously its why almost all of them are in the military. The other effect was to carry on with the story and actually develop the character. It would have been awkward and felt forced if he had to vocalize his reasons for joining the military. That 45 seconds of footage was enough for most Americans (sorry its film by Americans for Americans in this sense) to sympathize with his cause and justifications.
Given how you need to wait 15 minutes to find out if he did shoot the kid with grenade at the start, I can see why, in the spirit of the films cinematography It would show the two towers then BAM sandstorm and shit show in the desert of Iraq. The footage and that cut was enough of an explanation to develop the character instead of having 2 other scenes and 15 minutes of WHY he joined the military.
This film actually paints Chris Kyle in a controversial light compared to how others knew him. I dont like that so much, but what Mr. Eastwood does do rather well is getting his cinematography to tell the story (think Black Hawk Down when they leave the FOB to assault the building in the City, there is only subtle music and next to no sound but it creates a tense atmosphere) and getting military facts as close to real as possible (even tho American Sniper falls short on this part).
So, what im trying to say, don't read into that scene to much.
Oh yea, I do have a degree of bias even tho I try to hold that back when making comments such as this. I was in the US Military, I am MURIKAN, I like Guns and cups that hold more liquid content than your stomach could ever hold. But I knew some people that knew Chris Kyle and I grew up around that culture and environment.