Definition of a Sport (noun)-An activity involving PHYSICAL exertion and SKILLS that is governed by a set of RULES or customs and often undertaken COMPETITIVELY.

PHYSICAL?- Working out getting into shape. Try running with a sousaphone.
SKILL?- Marching difficult drill with precision while playing a cadence or songs by memory. Also dancing as a group.
RULES?- It Usualy varies slightly by region and style but yes MARCHING BAND does indeed have a set of ruled that each BAND must follow, breaking the rules results in penalties that hurt your score at competition.
COMPETITION?- Oh yes, there are some competitions all over the place. So check one out some time.
PRIZE?- All bands get some type of recognition and or prize depending on the rules.

So according to the definition of a sport MARCHING BAND is a sport