"My hobby is sport" is correct English usage. Using "sports" is more the American usage whereas using the singular is more common and correct in British usage.
I'm checking about it now. I thought when talking about sports in general, it has to be "sports". Are you a native speaker? I asked other contributors to help out :)
Update: I was told that "My hobby is sport" is incorrect, and it should be "sports". Any more comments?
Suggestions for fix to be recorded - "Report a Problem". Here is only a discussion - "Discuss sentence" . Sorry.