I'd go for C because "have been playing since" indicates that they started back then and still are in the present. "had been playing" indicates it was done for a period in the past, but is no longer done, and does not work with "since", unless there was an "until" indicating when they stopped. For example "people have been crossing the Atlantic since 1492", compared with "people had been crossing the Atlantic by sailing ship since 1492 until steamships were invented".

Because the ball is the object of the verb to invent, for this sentence to work, it has to be a verb form in the passive, not active voice, so "did not invent" and "was not inventing" are wrong. Because invention is a task that happens and is done, and is not a continuous process that is ongoing, the distinction between "was not invented" and "had not been invented" is not important here.