Well, Bionicle is different for everyone. That's why I said earlier that for some people the sets are the center of Bionicle, and since this isn't something that involves LEGO in any official capacity, then it isn't the project for them. There's a lot of components that make up Bionicle, so it's not just one thing, so asking what one thing makes something Bionicle is a bit of a futile question to ask. It's much more complex than that.
For me, the things I like most about Bionicle is the atmosphere, the aesthetics, and the non-traditional storytelling. Anything with those elements is Bionicle to me (this might be why I like G2 more than most people; it had all those elements enough for me to make it Bionicle).
If you want to know my hypothetical, or what I'd dare to re-imagine Bionicle as, if you will, it'd be a multi-media creative franchise. Think about the scope of creative IPs like the SCP Foundation. There's a main sort of "canon" in the articles, sure, but it's composed of many forms of media that people like. There are SCP videos, other kinds of stories, fan art, fan models, video games, comics. I'd love to see something similar with Bionicle, a universe dedicated to telling its story through all these new, neat, "post-cinema" media. VR could be a component, for instance?
My imagination was sparked by Faber's previous imagery of Antarctica. I'd love to see a new Bionicle with a kind of gritty, industrial aesthetic combined with that frozen landscape. A spunky group of robots with powers on a mission to save the world from a mysterious danger. It's got a similar aesthetic feel, the non-traditional storytelling, and a similar kind of atmosphere that makes it Bionicle to me.
I think what's important, though, is to be more open-minded as to what Bionicle can be. It might have some of the elements we like, it might have all, or it might have none and become a new thing. We shouldn't reject it because of that, though, because it's still attempting to honor that Bionicle spirit.