Sport involves physical skill, a game can be played via telling someone else what to do.
E.G Chess is a game, a grand master could tell me which pieces to move and make me win… it wouldn’t be me winning it would be the person controlling me.
However, take darts for example… this is a sport, you can tell me to throw treble 20… but without the physical skill to do it I will still lose.
Physical skill = sport
Can be played through a rote dictation = game
I’d argue Fishing and Shooting are sports, just not ones that requre endurance. They still require a physical ability to do something better than the next person. If I say shoot the bulls eye, only a skilled marksman would be able to do it.
Fishing is slightly debateable.