cockfighting vs blood sport

cockfighting and blood sport both are nouns.

Word	Noun	Adjective	Verb	Adverb
cockfighting	Yes	No	No	No
blood sport	Yes	No	No	No

As nouns, blood sport is a hypernym of cockfighting; that is, blood sport is a word with a broader meaning than cockfighting:

cockfighting: participation in the sport of matching gamecocks in a cockfight
blood sport: sport that involves killing animals (especially hunting)

cockfighting (noun)	blood sport (noun)
participation in the sport of matching gamecocks in a cockfight	sport that involves killing animals (especially hunting)