It seems to me that Tyrannosaurus rex was not the brightest species. This is probably why it died out.
Tall people are actually good in a very significant majority of sports. Body height is the major determinant of sports success overall. If it were not true, Olympic athletes wouldn't be markedly taller than their native population. (They are, by ca. 5-6 cm on average.)
Among the major Olympic sports, only long distance running, gymnastics, diving, trampoline, badminton, table tennis, mountain biking and partly road cycling (depending on terrain) require body height below 180 cm. You can add weight categories in martial and strength sports, but these are largely bogus and artifical activities for small-sized people.
At Winter Olympics, you could find more sports with lower height requirements (mainly figure skating, short-distance speed skating, ski jumping and various acrobatic events), but understandably, the international competition is inevitably lower as well.
Olympic sports that are most demanding in terms of body height (190+ cm) are basketball, volleyball, handball, waterpolo, short-distance swimming (crawl), rowing, heavyweight divisions of combat sports (taekwondo, boxing, judo), bobsledding, high jump, discus throw, shot put.
BTW, height in running is a damn important factor! Short-distance sprinters are not too tall on average (about 181-182 cm), because excessive height would hamper acceleration. The longer the distance, the taller the runners are: In the 400 m, they are the tallest (at least 185 cm on average), because this distance relies on anaerobic capacity that increases with body size.
After aerobic metabolism gets the upper hand (which happens after ca. 55-72 seconds, according to mathematical estimations), runners again become smaller: About 180-181 cm in the 800 m, about 176-178 cm in the 1500 m. (And I should add that around 1990, the average height of a 800 m runner was about 183 cm, and that of a 1500 m runners was ca. 180 cm. The African participation pulled the means down, but as we know, clean times are not faster than in mid-80's.) In the 10 000 m and the marathon, average height falls below 170 cm, because small body dimensions are closely tied with running economy.
And we shouldn't forget that height is very important in the hurdles: The average 110 m hurdler is about 186 cm tall (i.e. the tallest among all runners), the average 400 m hurdler is not much different from runners in the flat race (ca. 185 cm).
In summary, the current ethnic composition of athletic champions in the 400-1500 m doesn't fit the anthropometric data. In the 400-800 m it is really hilarious. Simply absurd. People often think that when the 400 m is a "sprint", it means that the dominant runners must come from the same nations that dominate the 100-200 m. This is wrong. The 400 m distance has markedly different requirements, both in terms of physiology and body type.
The most grotesque thing is that the available data on the muscle fiber composition don't indicate that there would be any marked physiological differences between Europeans and West Africans in this distance. Certainly not in women, because the muscle fiber composition in Europeans in vastus lateralis muscle (ca. 55% fast-twitch fibers) would just ideally fit in a race that is slightly anaerobic (i.e. lasting 50-55 seconds or so). In contrast, the muscle fiber composition in West African blacks would be closest to the 200-300 m.
For a long time, I was thinking over the roots of the current situation in the 400-1500 m. I couldn't grasp it. It was simply mindboggling. Moroccans and Kenyans, 171 cm tall, dominating the 800-1500 m?! Eventually, I had to resort to the simplest explanation: People in the industrialized world don't give a damn about track. Yes, it's so simple. And since that time, I don't take track results seriously anymore.