This has convinced me. Very well put together video.
I agree that it's the Fallen Hero timeline, but I think it's between OoT and ALttP. There are too many OoT and SS references for it to be after ALttP. Hyrule Historia says that the meadow that the Master Sword is found in in ALttP is the remains of a temple, which is most likely the Temple of Time, so it wouldn't be in a game set after. The Temple of Time is in a lesser state of ruin than in TP, which takes place 100 to a few hundred years after OoT, and it's surrounded by the ruins of OoT's Castle Town, including the fountain and possibly old Hyrule Castle.
ALBW also takes place after ALttP and would deeeeefinitely have mentioned this.
This game stars a Hero who failed. We already know of a Hero who failed in this timeline: the Hero of Time. The Master Sword isn't just worn down from the elements, most of the damage is chip damage from battle. He awakens from a 100 year slumber in a medical chamber wearing OoT-era Sheikah underpants.
NWR's main reason for thinking it's after ALttP is that Link has epic sideburns, but after 100 years in a stasis tank anyone would have longer hair. Wind Waker depicts the Hero of Time having epic sideburns:
http://cdn.vanillaforums.com/pennyarcade.vanillaforums.com/editor/om/dbwhlwpinf4a.jpg
This is the Champion Shirt, which is the main clothing we've seen Link wearing in BotW. People thought Link's armbands may have been Gerudo influenced since they are very similar to Ganon's in OoT, however it's possible Ganon had those armbands because he had the trust of King Hyrule. The colors are similar to those seen in the ancient advanced civilization in Skyward Sword.
My thoughts are that following the defeat of the Hero of Time, Zelda and the sages began trying to seal Ganon by themselves as a last resort. However, since Ganon had the complete triforce and the power of a god, that would be no easy task. They couldn't seal Ganon without Link stabbing him in the face when Ganon only had the Triforce of Power, so why would they be able to do it without him when Ganon had the whole thing? The entire purpose of the Master Sword is to counter the power of the Triforce. So they put Link in a medical chamber to heal and engaged in a 100 year long battle to keep Ganon contained.
The Old Man is probably the King of Hyrule. He looks near identical to King Hyrule from Wind Waker. Since he has no castle due to Ganon he's been living on the plateau watching over Link.
ALttP refers to Ganon as The Great Cataclysm. Cataclysm is a synonym for Calamity, and Ganon is referred to in BotW as Calamity Ganon. ALttP's backstory also refers to Ganon attacking the world as a smoke-like force, which is what Calamity Ganon looks like.
Another thing is that Zelda refers to Link as Hyrule's light that must once more shine upon the land, and Zelda mentions in OoT that she had a dream of Link as a light shining from the forests.
OoT:
"I had a dream... In the dream, dark storm clouds were billowing over the land of Hyrule... But suddenly, a ray of light shot out of the forest, parted the clouds, and lit up the ground... The Light turned into a figure holding a green and shining stone, followed by a fairy... I knew this was a prophecy that someone would come from the forest... Yes, I thought you might be the one..."
BotW:
"Link... you are the light- our light- that must shine upon Hyrule once again."