Technically, yeah. If any Undead Hajime transforms into is counted as a rider, then even his human form would be a Rider. Or you could say Hajime isn't even a rider, if you only consider those with a man-made belt a rider (which makes Kenzaki lose his rider status at the end of the show).
I think the show goes just with the fact that Mantis Undead looks like a rider (due to the design) and is Hajimes default battle form.

You could also argue that the Undeads couldnt be counted as Riders since the Ace of Heart Undead isnt the Rider. Hajime is. So no matter what Undead Chalice would use as a base it would still be Kamen Rider Chalice but the Undeads on their own are not.

Kenzaki is a different case, as his Blade form and the Beetle Undead are different.

They don't need a man-made belt (As that'd remove the rider status of Amazon, everyone from Hibiki, Shin, etc), it's just something that came to mind, is all.

So would that qualify Dragonfly and Wolf as forms for Chalice?

Technically yes they should be counted since thats how Chalice works.

Technically yes.

Also, the comment about the man-made belt was of course only considered in the context of Blade, not taking other riders in account.

Though Convoy's point is also valid. The show usually only counts Ace-Forms as Riders- except for Cerberus because that one was completely different.

Well not really.
That would be like saying the Voltron team are power rangers cause they wear matching uniforms each with different colors.

What's the relation to my question?

See:
Fact - Chalice is a Kamen Rider.
Fact - Hajime's (KR Chalice) Rider form is just the Mantis Undead (Ace of Hearts) with the Joker Buckle (There is no further alterations to the Mantis Undead's monster form other than he's wearing a buckle).

It leads to my question. Where does the criteria for being a Rider end?
Does the Mantis Undead always qualify as a Rider, with or without being scanned by the Joker Undead?
Do all Ace Undead qualify as Riders?
Or does simply being a Joker Undead mean you're a Rider, regardless of what card you're scanning?

I think the Joker-explanation might be the most logical one, as the Rider system in Blade was based on Joker's powers. So all that have Joker's powers or some that are similar are counted as riders. I guess.

Though the name "Kamen Rider Chalice" isn't used in the show at all, if I remember correctly. So basically, the show never confirms him as a rider.

It's confusing. It really is.

I can't remember whether Chalice is used as a name in series, but I'll accept the Joker explanation.