what kind of fight is the one mentioned here?
It  is an aerial battle between fighter aircraft conducted at close range.
Dogfight
 is an aerial battle between fighter aircraft conducted at close range.
indiana jones and the last crusade last scene In the last scene, a dogfight with Luftwaffe fighters ensues although Indy and Henry are forced to crash-land, they survive and successfully bring down their pursuers.
wiki:1898589
Dogfight [SEP] Introduction
A dogfight, or dog fight, is an aerial battle between fighter aircraft conducted at close range. Dogfighting first occurred in Mexico in 1913, shortly after the invention of the airplane. Until at least 1992, it was a component in every major war, despite beliefs after World War II that increasingly greater speeds and longer-range weapons would make dogfighting obsolete. Modern terminology for air-to-air combat is air combat maneuvering (ACM), which refers to tactical situations requiring the use of individual basic fighter maneuvers (BFM) to attack or evade one or more opponents. This differs from aerial warfare, which deals with the strategy involved in planning and executing various missions.