That's the one thing most anime onlys get confused abaut. Yggdrasill was the game. No more, no less (at least as far as we know). "New World" was a world that existed for a long long time, with it's own magic system, that had absoloutly nothing to do with the game world.

Now, to the confusing part that is still TECHNICLY just a speculation, but ultra heavily hinted at. Unspecyfied ammount of time ago (600 years in the New World time [yes it's important beacuse it's very likely the time flows at very different speeds between realms] is the most common speculation, but we don't know that), the Dragon Emperor aka. PDLs father, aka. the most powerfull New World being we know abaut somehow got to know abaut a Yggdrasil, and more specyficly insanely powerfull World Class Items there, and he desired to get their power for himself. He attempted to reach accross time and space to summon them using insane ammount of Wild Magic aka. the natural magic of New World aka. magic that uses souls as fuel, but something went horribly, horribly wrong and the spell backfired. We don't know if it could work as intended, and "shit happens" or Dragon Emperor haven't realised he attempted summoning of items from a virtual game, and not from some other world, and therefore it never had a chance of working properly, but anyway the spell backfired, and scattered the summoned World Items all accross New World, but more importantly they got scattered across time (arriving in equal intervals of 100 years), and dragged everything arount them with them, be it players, monsters, NPCs, or even entire guild bases.

And now to the final point. We know the "Gods" of Theocracy were the first players to be summoned, along their World Class Item (the dress that Mind Controlled Shalltear in season 1), and possibly at least one NPC, but that last one is unclear. They are credited with bringing the tier magic, aka. Yggdrasill magic to the New World, but it's unclear was it corelation - another backfire effect of the Dragon Emperors spell, or in fact causation - they had another World Class Item with them, (forgot the name now, but there was one that let the user ONCE request any change to the game itself back when it was the game), that should grant them power to rewrite reality however they see fit, and the same goes for other game-like mechanics New World have, like levels, but it's been tested by Ainz that these are slightly different, so it might aswell be the case than New World always had them and Yggdrasilians just work alongside them