Lyrics

In the normal ending, Miku cries in front of her creator's grave, makes the flowerpot grow, and joins him in heaven as usual. However, in the alternate ending, she trips, drops the flowerpot, and breaks it. Then an angel Luka shows up.
"At the end of your journey, you dream... I, too, no longer have the one I love." "..." "But... You are different. At the least, your beloved..." "?"
Luka does something fancy and Miku's Master appears sleeping in front of her.
"If he's merely "resting in peace"... then you should wake him up."
Miku sings, he wakes up, and she hugs him. "Hello, ohello... Hello, ohello...!" "I'm sorry I left you alone. I wanted you here..." "But, the flowerpot..." "It's fine. We can just water it again. As long as I'm with you... however many years it might take... I'm sure..."
Miku and her Master water flowerpots all over the world. As they water the broken one back in the shelter, a letter arrives in the mailbox: "Keep you and your beloved precious."

I mean this PV, by the way. The original one.
3390 (the high score on the title screen) is "sa-sa-ku-re." Oh, you.
573 is "go-na-mi," the Konami number. It's the default high score in some of their games, among other things.
2216 is "ni-ni-i-ro," but could possibly be going for "nanairo" (rainbow), considering Sasakure's Nanairo Adventure.
3594 is "san-go-ku-shi," the Records of the Three Kingdoms. Um, maybe.
5656 is "go-ro-go-ro," a rumbling sound effect.
7188 is "na-i-ya-ya," which is probably either for "nai" (gone) or "iya" (no), both of which sorta apply to Miku finding her Master's grave.
9071 is "ku-re-na-i," crimson.
1059 is "ten-go-ku," heaven. (Yes, you actually have to read 10 as "ten.")
Ones that either don't have puns or I don't get them: 1394(0), 3776(0), 4410(0), 6256(0), 8823(0), 9632(0).

For an unknown reason (Miku's Master heard it could have been diplomatic issues, conspiracy with some country, or surmounting tension), a world war begins. Aliens may play a part in the war as well. I'm... not really sure how, though.

Rin, in The Weekend's Coming!, tries to ignore the stupidity of the adults fighting the war and focus on her love for her boyfriend. However, her boyfriend leaves, presumably to go fight in the war. Rin grows depressed and supposes that, with the feelings of love she never quite told him and now never can, she should write letters to spread around the world that might give people hope.

Miku's Master later finds one of Rin's letters, addressed to "you and your beloved." Who knows when this is, or how much he learns about her, but it's unlikely they meet, as he never learns her name (only calling her "the girl"). Meanwhile, Gumi sings about how she got dragged into the war and has to fight for whatever the adults deem to be right in Our 16-Bit Wars.

During the war, the Master probably meets Luka (or creates her, even, since she cares for him and he knows how to put her in sleep mode) and creates Miku if he hasn't already.

After five years of war, on The Day the Sky Fell, one country - unknown which - fires a missile. Soon after it hits, all the countries launch their missiles in retaliation, the sky goes bright, and... The Sky Falls. In actuality, this probably means the complete destruction of the atmosphere, which turns the sky anything but blue, makes rain into something harmful, and probably pollutes the air since people seem to get exhausted going anywhere.

The only apparent survivors of The Day the Sky Fell are those in the Shelters: Miku's Master, Miku, Rin (maybe), Luka, and at least 37 other humans, presumably in higher-numbered Shelters. Of the named survivors, the former two are in Shelter 2 and the latter two are in Shelter 1. Shelter 2 seems relatively unharmed by the sky falling; it loses communication with the others, but that's probably just due to the gray clouds and their survivors dying out. Shelter 1 doesn't fare as well, however, as Luka is damaged and Rin dies (one way or another).

Miku's Master goes to Shelter 1 and Luka informs him that Rin died somehow, then perhaps starts softly singing Wanderlast (and her "endless song" may continue until she's put to sleep). The remaining humans (and non-flowerpot plants, and animals) eventually die off - a fact Miku's Master learns from the satellites - leaving him to be the last life on earth. He puts Miku and Luka in sleep mode (apparently telling Miku about the flowerpot just before doing so) and dies in his sleep days later.

Miku wakes up after her Master's death and goes in search of him. (How this is supposed to make sense in the game, where she reads his records that make it pretty clear he died, I'm not sure.) In *Hello, Planet, Miku travels what's left of the world and says hello to everything she sees, collapses at her Master's grave, and cries into the flowerpot, making it grow and send her up to heaven. (Whether that's a dream or what.)

For some odd reason (how did they grow wings in Weekend, anyway?!), one of Rin's letters (maybe even the same one Miku's Master found) then shows up in the mailbox. It apparently reads, as the original video's description says, "Keep you and your beloved precious. Oh hello, ohello."

And *Goodbye, World End... Honestly, it kinda sounds like Miku singing about the reality of the alternate ending**, strangely enough.