Is chess a sport? If yes, then why? Sometimes (e.g. at some schools) chess is considered to be a sport. Is chess a sport? I view sport as a physical activity.

For instance, if a doctor asks you "Are you doing any sports?" would your answer "Yes, I play chess twice a week!"? It sounds a bit strange in my ears.

Is chess a sport?`

If yes, then why and to what extent?

Thanks!
The question of whether chess is a sport depends entirely on the context of the question. In certain situations, it may be useful to classify chess as a sport. For example, as you mention, in some schools chess is considered a sport because it matches the requirements of a sport in that context - an activity that pupils can engage in outside of academic learning that essentially keeps them out of trouble. Yet in other contexts, as when sport means to exercise some muscle group or improve fitness or some physical ability, chess would not typically be considered a sport. 

On a deeper, philosophical level, the question is meaningless. "Sport" has no objective, unambiguous definition, it is a cultural concept that changes in meaning depending on time, culture, fashion and many other factors.