there is a factual problem with the summary...
It is a bad summary, but only because the wording is ambiguous, not that it's factually incorrect. The statement you're objecting to is perfectly correct in one interpretation, and dead wrong in another. Your own counter-statement, "it is not required of the opponent to play rock 50% of the time," is equally ambiguous. In fact, 50% of the time (assuming a fair coin), the opponent is required to play rock, so it's true that "it is required of the opponent to play rock, 50% of the time". Leaving out the comma yields a true sentence (assuming the correct interpretation is chosen of the now even more ambiguous sentence) that contradicts the quoted sentence of yours, assuming you parse your sentence as "it is not required: that the opponent play rock 50% of the time", but does not contradict it at all if your sentence is parsed "it is not required that the opponent play rock, 50% of the time", since 50% of the time, the opponent can choose freely, and thus is 50% of the time, is not required to make any particular choice. So, both the summary and your explanation of what's wrong with it contain statements that not factually incorrect, just ambiguously worded such that a reader might interpret it to mean something that is incorrect rather than something that is correct.
This is a textbook example of why programming computers in plain English would be a monstrously bad idea.