What does 战斗机 in this line mean?
"fighter jet" is something originally from an ad that was popular many years ago:

波导手机，手机中的战斗机 

The ad aims to emphasize the extent to which their cell phones are more superior than others (fighter jets are much faster than normal jets). It had repeated many times for a long period, so many people got to know it very well. Since then, "fighter jet" is also used in other cases, such as the case you mentioned "备胎中的战斗机". Here it means "the best spare-tire among all the spare-tires".