Sport: an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
Common opinion is that e-sports are not physically exhausting, and so do not qualify as sports. This is far from the truth, and the people who play video games competitively will routinely train themselves to exhaustion practicing the very same things anyone in any competitive physical sport would: reaction time, hand-eye coordination, endurance and stamina, and psychological fortitude, along with the strategy and planning competitive video games are typically known for. They do this because if they don't, they'll be beaten by the people who do; and, additionally, as with any skill or exercise, you can only get better by always pushing further.
It is the one sport where strength isn't a factor, though. It's all speed, reflexes, rapid decision making, overall strategy and ability to adapt on the fly, and all to the point where anyone past the age of 25 is at a severe disadvantage due to the body slowing down with age. Keeping the body in peak physical condition gives a noticeable advantage in reaction times and your muscle's ability to resist fatigue, and it's a proven fact that people who work out have faster reaction times and healthier brains than the people who don't.
I guess a good comparison is major league baseball vs you and your dad playing catch in the backyard.