무슨 is a direct modifier. In other words, it comes directly in front of nouns.
examples:
“무슨 음식을 좋아해요?” (What foods do you like)
“무슨 영화가재미있어요?” (What movie is interesting)
무엇 can NEVER be used alone. It always be followed by a particle even in casual speech.
examples:
“무엇을 좋아해요?” (What do you like?)
“무엇이 재미있어요?” (What is interesting)
무슨 is used for nouns which sport is a noun so its used because it modifies it, if that makes sense.
I hope i helped you out.