You Have to Burn The Rope/WMG

As this is a WMG page, blatant spoilers will be unmarked, so proceed with caution.

The game has a Truman Show Plot.
You are an invincible being completing a ridiculously easy task against an enemy that will not damage you at all. The "director" can't risk losing you, so they make it impossible to lose, but they gave you the task of burning the rope as a main story arc of the show.

Indykirby will be in the final Indiana Jones movie.
The hat really is Indy's hat.

Indykirby is Kirby's father.
Kirby must have gotten the eyes from his mother.

Indykirby is Ash's father.
And a Jiglypuff with a hat. The axes double as microphones, as his other son's microphone doubles as a permanent marker.
 * Um, Jigglypuff from the anime is a girl.
 * ...There are other Jigglypuff you know.
 * All Jigglypuffs are female. Unless you make that Hanako/Delia was a male...
 * Actually, there are male Jigglypuff. There's just a 25% chance of finding one, you see.

You Have to Burn The Rope is a treatise against sexuality, or at least polygamy.
The Grinning Colossus, as the final boss, is a huge black phallic symbol. You defeat it by using the pink thing to transfer fire, a metaphor for STDs, to the thinner (and possibly shorter) pale-colored rope, which drops an entire chandelier of fire and wax onto the Grinning Colossus, destroying it. The eye-beams are a metaphor for the risk of pregnancy, the collision damage symbolizes how consentual sex has the same potential consequences as rape, and the final battle is reminiscent of conception (a sperm traveling into the womb and attacking an egg) and abortion/contraception (a little pink pill-shaped being goes into same womb and attacks the life inside). Most forms of sexuality are symbolized as bad (straight with the main character and the rope, gay with the rope/chandelier and the Grinning Colossus, lesbian with the main character and the symbolic tunnel/room shape, the rope and chandelier look exactly like a really oddly-shaped woman with dozens of limbs that dies while in a bondage situation, and polygamy, as represented by the relation of all the previously mentioned factors), and the very shape of the final dungeon and the long corridor leading to it seems to say "if you go down this path, bad things will happen."
 * This theory is made of win! I heartlily salute the troper who proposed it.
 * Uh... Freud Was Right?

You Have to Burn The Rope is a jab at overly difficult puzzle bosses.
Isn't this Word of God?

The rope is a lie!
You have to listen to all of the things you are told, by a voice that comes from the walls. You don't get your only useful item until partway through the game, and the last stage involves application of fire, and not getting burned. Coincidence? I think not. Even the "burning of the rope" makes the rope look fake! The rope burns from the top down no matter where you place the fire, almost like a prerecorded holographic playback, with the chandelier really dropping from a hook on the wall!

The ending credits song is a hallucination of the psychotic and evil player character.
You go into the home of the Grinning Colossus for the sole purpose of destroying it, and there isn't necessarily any way for the colossus to actually leave its home and cause havoc. Why would you be a hero for killing something that was sealed away or not even evil in the first place?
 * The hero was Genre Savvy enough to realize that Sealed Evil in A Can almost always escapes eventually. There was only one permanent solution: He had to burn the rope.

The entire game was a dream of Indiana Jones.
He wanted a single adventure without a car chase, tunnel boulder, or Phlebotinum Breakdown. He got it.
 * So... He dreams to be a hollow-eyed Kirby?
 * Duh. Who doesn't?

The Grinning Colossus is Not Quite Dead.
Or at least, he's found some way of fighting off Death

You don't really have to burn the rope.
It's more of a Urban Legend of Zelda than a Wild Mass Guessing at this point, but I'm working on it.
 * Since neither Indykirby or The Grinning Colossus can die if you don't burn the rope, you could have potentially fought him off indefinitely.

You Have to Burn The Rope is a cross between Dr. Mario and Osmosis Jones.
The entry hallway is the esophagus, the Grinning Colossus is a parasite, and the protagonist is a pill designed to kickstart whatever defensive mechanism the "body" has that the parasite evolved to avoid triggering.

The rope wants to get burned.
Think about it. How many items are really in that area? Who could have told you that You Have to Burn The Rope? Now, the instructions appear on the screen without text boxes, which generally indicates a telepathic or omnipresent voice. The Grinning Colossus would have no need of such vocalization, as his grin clearly indicates that he has a mouth of his own. This leaves our speakers as the rope or the chandelier. The chandelier, however, is attatched to the rope, indicating a strong friendship between the two. Even if it were to perform a Heroic Sacrifice, it would be far more likely to try and develop a plan that minimize the damage done to the rope (eg, You Have To Untie the Rope). The only possible explanation is this: The rope, tired of being constantly stretched taut, is committing Suicide By Cop. It is so desperate that it does not care that the chandelier will die as well; indeed, the rope will be happy to have its friend join it in the afterlife. The only death that can ensure the rope's complete and utter destruction is burning, so it creates a situation in which You Have to Burn The Rope and gives you instructions to that effect. The Grinning Colossus is, in fact, merely an illusion created by the rope to give you a motive to burn the rope.

You Have to Burn The Rope is the Mirror Universe of I Wanna Be the Guy
Which means that in the world of the former, there is a The Kid who wants to defeat an incredibly easy-to-beat The Guy, and in the world of the latter, there is an "Indykirby" that must go through a nearly impossible quest to destroy a Grinning Colossus with Cosmic Horror level power.
 * Chandeliers do not fall up!
 * They're really more like candelabras.
 * Is Eversion somewhere in the middle?
 * Eversion goes back and forth. Duh. It's Eversion.

Alternately, You Have to Burn The Rope is the Mirror Universe of Spelunky
Both feature an Indiana Jones Expy and monsters, but are complete opposites when it comes to difficulty.

You Have to Burn The Rope is a Lotus Eater Machine that The Kid is trapped in.
Maybe even after. Unfortunately, though both the Grinning Colossus and IndyKirby were meant to be invincible, he could Burn The Rope to kill it.

It doesn't matter if you burn the rope.
You'll still die trapped in a stone room deep underground with no exit.
 * Jossed..

Indykirby is Haruhi.
A Haruhi who got really frustrated with the world he/she was in, and wished for it to be easier.

The Grinning Colossus wanted Indykirby to kill him
Note that the Grinning Colossus is too big to get out of the room he is in. Tired of being stuck in the room for his entire existence, he summons Indykirby and gives him instructions on how to kill him, because he can't kill himself. He only attacks Indykirby to get him to get it over with already, which is why his attacks don't do any damage. He doesn't attempt to dodge the chandelier, in fact he makes sure he's hit by it. It's all an elaborate suicide scheme.

The torches are the real villains.
They couldn't get to the rope, the only flammable thing in the room, on their own. So they told you to burn the rope. This "coincidentally" killed the Grinning Colossus, the only thing keeping them trapped in their underground prison, without a means of locomotion such as IndyKirby to take them to the surface world. The Crowning Music was sarcastic: you didn't save anyone, and now there's nothing left for you to do but watch it burn.
 * You're right! There's a lyric in the song which clearly refers to the singer as "we".

That's not the whole game.
The awesome ending music is only for the Bad Ending. There's a secret exit somewhere in the cave, leading to an epic quest more awesome than, say, Cave Story.

The sings the credits song.
Since it's a parody of Portal and all...
 * Maybe he was telling us the instructions too, which kinda ties into one of the above WMGs.

The ending is And I Must Scream
Think about it. There's no way out. You can't die.
 * And now you are the new Grinning Colossus.

Winnings does nothing.
As this clearly shows, The Grinning Colossus survives and escapes to Loathing. In fact, he may originally be from there.

The Grinning Colossus is Not Quite Dead
He's merely the latest incarnation of a Sealed Evil in A Can. Every few thousand years, he tries to escape, and Indy Kirby has to venture into his dungeon and burn the rope.

Indy!Kirby is Kirby
He inhaled Indiana Jones sometime before the events of the game.

This game is a sequel to Shadow of the Colossus.
But set in a branching timeline from the one which leads to ICO, where, or at least until Indy!Kirby shows up centuries (based on his clothing) later and drops a chandelier right on top of the weak spot on his head. The being giving Indy!Kirby advice at the beginning is Dormin taking back up their old role