You are right, the popularity is because of Windows. But aside from the failed Surface RT, it's the only ISA they write an OS for. At that point, it doesn't matter if Intel is popular or not since you really have no choice. OS X is on Intel as well. Though iOS is a subset of OS X and runs on ARM.
As such, it isn't really Windows any more. It's the fact that Windows has all the applications that people want, including all the ones they've been using for ages. This was what killed RT.
MS is making W10 for ARM - W10 Mobile has Continuity, with a desktop, full featured universal apps, and the like. But no matter what, it won't run whatever 5-10-15-year-old x86/x64 application you might want it to. Unless Intel somehow starts licencing x86 for emulation, in which case - hooray! - you'll be able to run it, it'll just be incredibly buggy and slow.
x86 is here to stay, it'll be very relevant for at least another 10+ years. My guess is far more, considering the way Intel is proving there is such a thing as fast, power-efficient x86. Heck, they're even pushing x86 into phones!
The PC space needs AMD. The 'Intel v. ARM' thing is growing stale, and for the moment, Intel is even winning that. And ARM isn't looking like it'll scale up power-wise any time soon.