Using NPM stats is just not correct. I believe React to be about 2.5x larger than Vue rather than 6x.
As for what's next, I have a hard time envisioning anything usurping React any time soon. Its breed is basically the state of the art in UI paradigm and an active field of research. I'd put things like Elm in that cohort as well.
I think the better question is: what's next for React and its cohort?
When are we going to see these ideas appear first-class in Cocoa/UIKit/etc? When will we finally see "OOP is good for UIs" (OOP's final foothold in our dogma) lose out to "FP is good for UIs"? What's the next big thing inside the React ecosystem? How far can something mainstream like React move towards the strictness of something like Elm?
Vue looks like it's about 1.8x more popular in China.