I didn't realize this was a difference between British and American English, but I'm American and yes, here it is acceptable to omit "the" in certain cases, as in Su.Ki.'s example ("Johnny plays guitar"). However, it's also common to use "the." So go with your preference, or, to be on the safe side, just use "the" and you'll always be correct.

I think it is maybe American usage to omit 'the' but it is now very common and not really wrong. I would use 'the' - I'm english and older.

'the guitar' is the instrument/invention, like 'the internet' 'the dog' or 'the tyrannosaurus rex' It's used with abilities, like 'he can play the guitar' (= any guitar of course). 'play guitar' is about the action that someone does; what's he doing? He's playing guitar. or He plays piano in a band. Of course you can use the first meaning in these sentences too, but the difference is not really important. (it's nothing to do with British and American English)

I agree with Karen. In British English, it is usual to include the article, for example, "I've played the violin since I was a child". American English omits the article: "Johnny plays guitar". Both variants are acceptable.