Fun fact: मंगलवार comes from मंगल which is Hindi for Mars, by using Greek astrology, similarly like the names of the day of the week in Latin languages (e.g. martes is Tuesday in Spanish).
I take it this means "You play every Tuesday"; can it also mean "You are scheduled to play this coming Tuesday," as an English speaker might understand the translation?
It means 'You (generally) play on Tuesdays'. The latter meaning does not come across in the Hindi sentence. You have to say आप मंगलवार को खेलेंगे - 'You will play on Tuesday'.
Perhaps, then, the translation should be "on Tuesdays" as without context it sounds more like a future appointment. It seems, though, that "on Tuesday" alternates with "on Tuesdays" or simply "Tuesdays" all with the same meaning given the right context.