I believe that Marching band should be a sport because Wikipedia's definition of a sport is an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment
Physical exertion: working outdoors for ours doing on end drills
Skill: Requires repetitive training and memorization to achieve the desired technique
Individual team competing against others: The marching band goes not only to all football games to preform a halftime, but also goes to competitions to compete
Although your definition is entirely valid, you are applying it incorrectly. You are associating any form of physical activity with a sport. In that case, getting out of bed could be a sport. To elaborate, I do not disagree that being in a marching band involves some sort of physical activity. However, you are stretching the limits for that definition and associating any form of physical activity with a sport.
Your definition of physical exertion is very vague and completely incorrect. Using the Merriam-Webster definition, exertion is a laborious or perceptible effort, it has nothing to do with working outdoors doing endless drills.
Marching Bands resemble chess in the sense that they only meet half of the definition of a sport. Chess is a game that is compatible with competitions, however by using your definition it does not require any major physical exertion. The same goes for marching bands. There are marching band competitions but the type of physical activity is not reminiscent of a sport.
Another comparison could be made: marching bands and musicians. When musicians perform, for example violinists, it is not considered a sport, although it could also be competitive.