No, it obviously doesn't, this isn't even up for debate, we already have riders who don't apply to that, that ARE kamen riders, whether you like it or not, thats how it is, cut and dry.
It's the original concept, the one many series afterwards (including Heisei) take on.
As I said, yes they were called Kamen Riders. But in the true name, they are not. The reason they got the name was because of Toei's new marketing methods.
So are you seriously trying to tell me that the idea of having a rider get the Kamen Rider treatment (having someone use your own powers/abilities/cyborg enhancements against you. Whether working with the main bad guys or not) Is not in the least bit intriguing, like you really don't want to see that? They've done multiple times in sentai, so why not here? And sure while the evil rangers eventually turn good, with rider they obviously decided to explore what it would be like if this character didn't turn back. I'd say that idea is interesting, and while yeah they could just give them the Shadow Moon treatment, I would say that having someone evil also referring to themselves as a Kamen rider would be more interesting.
I'm not saying we should have a bunch of Shadow Moons. All I'm saying is that every evil guy with a belt and a bike should not be called a Kamen Rider. It's wrong to do it in my point of view. It doesn't take the fun away from them, it's not like Ohja was a great character because he kept calling himself a Rider. G4 was just a villain that didn't even use the name in the movie and he was great. I could go on.
Yes, I agree that it's interesting to have an evil character call themselves that, but as I said before it would only work if the villain in question thinks they're doing the right thing (e.g. Tiger, Orga/Kaixa, Eternal, Alternative).
Your definition seems to be only shaped by showa era series, therefor your definition doesn't have any real way to make sense of hesei era riders unless they fit perfectly into your narrow definition, which plenty don't. The writers for the various hesei series have really broadened the definition of what a kamen rider can be and it has made for some wonderful stories. If you don't want to count certain characters as riders go ahead, but they're still riders and no amount of debating will change that. you're putting in a lot of effort just for the sake of being stubborn,it kinda seems like a waste.
I didn't feel like giving a recent example, because you already did with Ryuki.
Yes, in the world of Blade or Ryuki anyone that uses the system will be a Kamen Rider, because it's just a name for the system there, a meaningless title (to which the protagonist himself gives a new meaning, but that's another topic).
As I said, we are looking at the whole franchise here, and for most of it, the title is meaningful, one that is given to good guys, it's not just the name of a suit.
Again, I agree that it's interesting to have a series where they did this. In fact, I loved it, but the problem arises when all of Kamen Rider starts becoming like this. Which is not anymore, but my fears are still there.
It's unique yes, but if overdone, it's just annoying.
I loved how J grows big, because it brings something unique and new to Kamen Rider. But had we had a bunch of Rider series in the 90's where they all grow giant, my opinion would be different.
Not the best comparison, I know, but all I'm saying is, while it's very entertaining to see a couple of series give that treatment to the name, it doesn't influence the whole franchise, and the true meaning is not that.
You can't just use Showa for your definition, the Heisei era exists and its definitions of what a kamen rider can be are just as legitimate, if not more so due to theirs being more recent. The definition of kamen rider is different for many series. For some its just a name tag, for some its a legitimate career, for some its their destined path, for some its their chance to fight for justice, for some its their chance to achieve their desires, and some use it because they desire power. once again, that definition is dated and doesn't make space for the sheer variety of fun and interesting characters that all share the mantle of kamen rider.
And let me remind you, only some series in the Heisei era change the definition for Kamen Rider: Ryuki, Blade, Kabuto & Decade. The others just don't even say those two words at all.