Much to learn you have, Grasshopper.
Okay, let's start with referencing other games. Leaving out any mention of the official timeline, how do the games reference each other? Well, going through chronological release order:
-Adventure of Link is a direct sequel to the first game
-Link's Awakening takes place after "a" game, in that he's already defeated Ganon. Most at the time guessed (correctly) that it took place after A Link to the Past.
-Ocarina of Time, even at the, um, time, was seen as taking place before all the other games. It's also at this point that the LoZ series really starts putting attention on narrative.
-Majora's Mask takes place directly after OoT.
-Oracle of Seasons/Ages were oddities at the time. I don't recall there being much consensus back then as to when they took place. After Link's defeated Ganon, yes, but that's really the only reference we had.
-Skipping around a bit, but then there's Four Swords, Four Swords Adventures, and Minish Cap. These games didn't relate to much outside their arc, but did relate within it. Minish Cap came first (which sets the stage for FS as part of its plot), then Four Swords, then Four Swords Adventures.
-Wind Waker takes place after Ocarina of Time, since OoT sets the stage for WW's backstory. Again, skipping ahead a bit, Phantom Hourglass takes place a few months after Wind Waker, and Spirit Tracks explicitly takes place a few generations after Phantom.
-Twilight Princess is a bit weird, in that it does take place after OoT if you squint, but only if you squint. We now know that Wind Waker and Twilight Princess are kind of 'parallel stories,' in that they both deal with Ganondorf after OoT, and in different ways, but Wind Waker leans on OoT far more heavily than TP does.
-Skyward Sword takes place at the beginning of everything. Even without an official timeline, it's explicitly an origin story for the entire series.
-A Link Between Worlds takes place explicitly after A Link to the Past (at the start of the game, you can see a summation of LttP), and Tri-Force Heroes happens a few months after ALBW
-Breath of the Wild takes place insanely far in the future, with elements of all three timelines. And Age of Calamity is an explicit prequel to the game (I think).
So, yeah. All of that is apparent without there being an official timeline. Prior to that, people debated how the overall game series linked together. Some imagined a single timeline, some a split timeline, no-one ever guessed about a third timeline (which, in fairness, is Nintendo pulling stuff out of its arse). However, the above are why the idea of "each game is its own Link/story" doesn't work, because there was always connectivity between games. Even with different Links, that still doesn't work, because for instance, OoT and WW Links are separate, but Wind Waker explicitly occurs after OoT.