No, chess is NOT a sport.
Many types of competition exist such as chess, auto-racing, debating, etc. which are clearly NOT sports. Bowling, however, and marbles (to take the worst possible examples) and archery and even target-shooting with guns and rifles are sports because of the demanding and over-riding physical element missing from chess, auto-racing, debating etc. We love a struggle whether participating or witnessing and all such struggles or competitions have sportlike features. However, sports at their base are physical interactions and may NOT always be competitive (e.g. hunting, fishing, hiking, mountain climbing, scuba diving, etc.) at all. Can some non-sports become sports? The 24-hour races in Europe can be understood to be sports, if for no other reason than their marathonlike-aspects which take the races into a truly demanding physical realm.
Although i mostly agree with you, i don't see the "demanding physical realm" in sports like fishing and hunting, but i agree underwater hunting or spearfishing is a physical demanding sport.
OK, let's get something straight here. Hunting and fishing are competitive sports, as are auto racing, hiking and mountain climbing. All of them have significant physical aspects even though for some of them, endurance is the greatest competitive asset. In any case, any one of them will get you physically beat up.
Chess is a game of endurance, especially otb. But because it doesn't require great physical effort (unless, of course, it's a case of finding yourself having to restrain your natural impulse to strangle your opponent for being a bonehead), it's not considered a sport, per se.
LoL, good question! Maybe ....