Well this chapter finally explicitly confirms that the anti-magic and the swords were originally two completely different entities.
So the 5-leaf grimoire was originally Real Licht's 4-leaf grimoire that contained Sword Magic. Due to the events 500 years ago the grimoire got corrupted and turned into a 5-leaf one, however the devil was never able to claim it and, as far as we know, it wouldn't be claimed till Aster came around.
Now the biggest mystery that remains here is when and how exactly the unknown anti-magic demon ended up in this equation? Till recently the most obvious explanation was that it was the summoned giant demon from 500 years ago, only we know now that that's a transformed Light and what's more it didn't use any kind of anti-magic. In addition no one seems to have any kind of clue about this demon, not even the devil who orchestrated all of this, this while you would think something like anti-magic is rather characteristic.
Weird though that the demon in question hasn't done anything this arc yet. On one hand this was probably done intentional to avoid to much parallel with Naruto and Kurama, on the other hand I can't imagine there have been many instances demons met each other...