I mean if we're arguing semantics about the word then I guess Mihawk's title doesn't count for anyone who uses a spear, trident, naginata etc because he's the World's Strongest Swordsman, not the World's Strongest Bladesman.
Ofcourse it doesn't but it ain't a big deal, the only Saijo so far which is not a Sword is Whitebeard's.
But we aren't arguing semantics here lol - Meito's are Blades, period. There is no world where a Club is called a Meito.
It's not even just Kaido's club, Yamato's club and Kanjuro's paintbrush is on it.
I mean.. what do you want them to do? Make another page for just these 3 weapons?
But in the same databooks itself, there is an emphasis on the strength of a weapon's wielder when talking about a weapon.
Or the scan of Kaidou's & Law's weapons that you posted.
To no one's surprise, only the strongest characters have Supreme Grade Blades.
The Shodai is not only a Saijo, it is also a confirmed Cursed Blade/Unruly Blade.
I cannot imagine Enma requiring more effort from a user to be tamed than a Blade which is superior in every way.