Oh, oh my.

I hadn't seen the movie up to this point, but that is pretty darned awful.

Okay, at the beginning of the war, pilots did fire handguns (and rifles and shotguns) at each other. They did this because they had no other option other than ramming to bring down an opponent. Once interrupter/synchronizer gears were invented that allowed machine guns to fire through the propeller arc, this practice went away. Some pilots still carried some sort of handgun--either to kill themselves if they caught flame or to defend themselves after being shot down--but their usage in combat is highly problematic. It is difficult to hit a target at anything but short range with a handgun on the ground. Add in both target and shooter moving in three dimensions and you have an incredibly difficult shot. This would not differ between triplanes and biplanes.

After the first few months of the war (in which there were no triplanes as depicted in this scene), I have seen no accounts of even firing at another plane with a handgun, much less scoring a hit (and a headshot at that). It is possible in Hollywood, but it would take a miracle to pull it off in real life In addition, why would the enemy pilot not react to the maneuver by the shooter, or make any control input that would spoil the shot (up or down on the stick would work, as would kicking the rudder in either direction)?

Wow I knew these pioneer pilots were brave but had no idea how brutal their situation could be. Thank you everyone for your informative answers so far