How is NieR connected to Drakengard?

NieR is a sequel in disguise. Its world descends from Ending E of Drakengard (2003), the strangest of that game's five endings. In it, the hero Caim and his dragon Angelus pursue the monstrous Queen-beast through a rift and finish their war in the skies over modern Tokyo, in 2003. They win. Then Japanese Self-Defense Force jets, scrambling against two unidentified flying monsters, shoot them down. Angelus dies impaled on Tokyo Tower.

That is where NieR's history begins. The Queen-beast's remains brought something into the world that had never existed there: magic, and with it a plague, White Chlorination Syndrome, which turned its victims to salt or slaves. Humanity's answer, centuries of desperate science, became Project Gestalt, and the broken world the project left behind, some thirteen centuries later, is the world NieR walks through. Every ruin and every rule of that world runs back to a dragon falling on Tokyo.

The detail worth keeping: by the developers' own retelling, Ending E began as a joke ending, a rhythm game duel over Tokyo that nobody expected to matter. It became the foundation of a series. When the joke ending is load bearing, the whole building leans interestingly, and NieR has been leaning, beautifully, ever since.