Except that the people who are have translated it are saying it directly says that that timeline is caused by "The Hero of Time is Defeated."
Personally I think this can still be the case without it being a Game Over situation. Suppose that child Link never receives the Master Sword and thus never "time travels;" eventually Ganon would defeat him in that timeline.
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(10:17:09 PM) Ed Bellis: i think pac-man just keeps repeating, for instance
(10:17:26 PM) ertyu: ya well tell that to billy michtlle