First off, one of the editors of the Hyrule Historia, the artbook this is from, is Eiji Aonuma. So you can't claim this to be unofficial.
Secondly, the "defeated" timeline, even as described in the book, is more of a "removed" timeline. As in, Link is removed from the equation in some way.
This also means that you're wrong on that, Max. Because "defeated" isn't the right terminology, it also means that there isn't an infinite amount of endings. All the "Ganon rules over a world cast into darkness" endings aren't made any more canon by this timeline than they were previously. Which is to say that they are non-canon. Just because an event CAN happen doesn't make it canon.
Here, have a translation of it.
As you can see, the timeline does indeed split three ways. Basically, it's like this.
TIMELINE 1: LTTP AND BEYOND
Link, as a kid, places the Kokiri Emerald, Goron Ruby, and Zora Sapphire in the Temple of Time and pulls the Master Sword from its pedestal. This removes him from the current timeline. In this timeline, there is no Hero of Time to stop Ganon. As such, he gains the full Triforce and turns the Sacred Realm into the Dark World. This is the Imprisoning War of LttP's past. When another Hero arrives years later (during LttP) Ganon doesn't think much of it originally due to the fact that he's never faced a hero at all.
TIMELINE 2: MM AND BEYOND
Link does defeat Ganon as an adult, and Zelda sends him back to the time when he was a kid. However, the timeline he is sent back to is divergent from his original one (the original one leads to LttP). While Link goes to Termina, the sages go to seal Ganon away. These events are what are referenced by the Sages in TP (and where one of them is slain).
TIMELINE 3: WW AND BEYOND
Link remains an adult after defeating Ganon. However, when the time came for another hero, one did not appear. This leads to the flooding of Hyrule and ultimately Wind Waker's events.
This explanation does seem to gloss over how Link can have the Master Sword in the original timeline (the "defeated/removed" one), but I think I've figured out how to explain that one. Basically, what if Link were removed from the timeline in some way and the Master Sword remained where it was in the Temple of Time, untouched for years. This would allow Ganon to get the Triforce unchecked and cause the Imprisoning War to occur (which leads to LttP).