As an American speaker, I would say both "I play piano" (to indicate "I have that skill") and "I play the piano" (either to express that I have the skill, or to say that I'm playing a particular piano). I would not say "go to hospital," though; I would always use an article. But "go to hospital" definitely does sound British to my American ear. Maybe a British speaker can verify that.
I agree that it sounds unnatural, so I removed this option from the default translations, now the default ones are only with "a" or "the". Still left it as an acceptable answer because I don't think there is such a thing as "more correct" :) It's either incorrect - then it should be removed, or it can be just less common or regional, then it should stay but not be a default answer.
Are you a native speaker? What would you say? It's correct but less common or incorrect?