"Heaven's cross...Is it the "Grand Cross" that occurred this summer? Is...this...some sort of prophecy?"
Nyarlathotep dictated the poem to Sudou and made him believe that it was a prophecy from Maian aliens. Sudou then conversely passed it to Akinari Kashihara, so he could add it to the supposedly mystical tome he was writing, In Lak'ech. In reality, the events in the prophecy were bogus and nonsensical, but were being transformed into reality by Nyarlathotep and his servants in order to rig his bet with Philemon, showing that humanity would ultimately destroy itself.
When the time came, he used the Joker's escapades along with those of the Masked Circle to ensure the Oracle's prophecies came to pass, ensuring reality was weakened enough in the area of Sumaru City so the release of In Lak'ech would inevitably allow the creation/return of the Fuhrer and his Last Battalion.
This supplied Nyarlathotep with a powerful, organized military force he hoped would reach Mount Katatsumuri and reach the core of Sumaru's powers. While the bulk of the Battalion's forces was destroyed before reaching the location, Nyarlathotep himself, disguised as the Fuhrer, did manage to reach said core and force a confrontation between himself and Philemon's champions. While he lost, he had previously influenced the deranged teacher Maya Okamura to kill Maya Amano with the Spear of Destiny, fulfilling one of the last lines of the poem and causing the Grand Cross to occur, halting the Earth's rotation and subsequently leading to its destruction from the violent inertia of all on the surface of the planet.
Only Sumaru City remained untouched by the destruction of the planet, as Xibalba had moved it out of the path of the debris and was shielding it from the extreme winds, leaving it the only vestige of humanity left floating above the now-dead Earth.
However, Philemon appeared to the group of friends and gave them the possibility to negate the timeline by ensuring they had never met. All but Tatsuya Suou agreed, creating the Eternal Punishment timeline and killing the Innocent Sin one, fulfilling the last line of the poem. However, the dead timeline remained a threat due to Suou's refusal to surrender his memories of his friends, and became a major plot point known as the Other Side.
In Eternal Punishment, due to In Lak'ech never being written, the Oracle failed to come true, although it was seen written on the walls of Sudou's room in the Sanitarium.
The seven Pleiades set the frozen time free
Wild dance, shadowed festival, foreign song ensue
As flames of expiation light the heavens
The lion's roar echoes far and wide
Five skulls glow in the depths of the earth
The holy cross shines high up in the sky
Once the star comes to a complete halt
The Maia Maiden's heart stops with it
What then remains is paradise on earth
Marking the end and a new beginning
The twinkling star of Pleiades sets time in motion;
Dance of pleasure, Feast of shadow, Tongue of stranger,
Atonement lights above.
The lion's roar echoes throughout...
The 5 skulls shine in Hades...
The holy cross shines in the Heavens...
The moment the stars stop rising...
The beat of the virgin Maia also ceases...
Paradise remains on Earth...
(The last verse is intentionally missing.)
享楽の舞 影達の宴 異国の詠