Maybe Fray's account of history isn't totally accurate, similar to how the Watchers' journals left out things and got some things wrong? I mean, maybe the "one great slayer" and the "enormous apocalypse" do refer to Buffy and "Chosen," but the end of magic and demons wasn't until later, but over time they got conflated into one huge battle.

There's also the tenuous connection that the fight with the First resulted in the activation of all Slayers, the activation of all Slayers prompted the rise of Twilight, and if Twilight succeeds, that will be the end of magic... so technically the result of "Chosen" is the end of magic, just with a few extra steps involved.

ETA: And clearly, beer_good_foamy is one step ahead of me, lol.