If the only reason you're sweating is because you're out in the sun then I'm sorry, that's not a sport, just like chess is not a sport even though it requires skills, training and effort.
If Alexis Lagan and Katelyn Abeln can compete 1v1 in the same category then I'm sorry to inform you that physical fitness isn't a criteria for whatever the competition is and we're not talking about a sport.
It does require phisical skill. You have to aim, perfect hand eye coordination, muscle memory, breath control. A sport doesn't require a full body workout, if it did than bob sleighing or dressage or table tennis wouldn't be sports either. Sport is about physical fitness but also about teamwork, competition, perseverance and much more.
It's like saying deathmetal isn't music, because you can't understand the words they sing.
So archery is a sport because it requires effort, but the effort isn't the part that makes archery hard? Olympic archers don't struggle with pulling the bowstring, they struggle with aiming the bow to get fractions of a point.
If they ran a lap in between shots during the shooting sports would you call that a sport?
sport is a contractive ellision of disport, from the Latin desport meaning "to carry away," i.e. a pastime in which you get carried away, or a game with equipment you can carry around.
All dictionaries describe sports as games of athleticism and/or skill.
If you get too prescriptive of your definition then things like running, swimming, karate aren't sports because they don't have equipment you can carry, or if shooting has no "athleticism", wouldn't it be fair to say that the 100m dash has no particular "skill" and thus is also not a sport.
If that sounds too ridiculous, maybe you should reconsider your position.
Have you also considered Diogenes' "Behold - A Man!" when trying to define sports?
noun
plural noun: sports
1.
an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
"team sports such as baseball and soccer"
Can't believe how exhausted they look! I feel the same way after spending the day sitting in my chair working an office job, maybe I should start calling that a sport!