By definition it is, actually:
From thefreedictionary.com site:
sport (spôrt, sp rt)
n.
1.
a. Physical activity that is governed by a set of rules or customs and often engaged in competitively.
b. A particular form of this activity.
2. An activity involving physical exertion and skill that is governed by a set of rules or customs and often undertaken competitively.
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From Wikipedia:
Sport is activity that is governed by a set of rules or customs and often engaged in competitively. Sports commonly refer to activities where the physical capabilities of the competitor are the sole or primary determiner of the outcome (winning or losing), but the term is also used to include activities such as mind sports (a common name for some card games and board games with little to no element of chance) and motor sports where mental acuity or equipment quality are major factors. Sport is commonly defined as an organized, competitive and skillful physical activity requiring commitment and fair play. Sports differ from games based on levels of organization and profit (not always monetary). Accurate records are kept and updated, while failures and accomplishments are widely announced in sport news.
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From the yourdictionary.com site:
sport (spôrt)
noun
1. any activity or experience that gives enjoyment or recreation; pastime; diversion
2. such an activity, esp. when competitive, requiring more or less vigorous bodily exertion and carried on, sometimes as a profession, according to some traditional form or set of rules, whether outdoors, as football, golf, etc., or indoors, as basketball, bowling, etc.
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And then again….we could always say that baseball, football, hockey, etc. are only just "games".