Intel's 120mm2 Core chip is built on a smaller process than the ARM based competition meaning there are far more transistors on that $200 chip than the one you are comparing it to. Also keep in mind that Intel doesn't need to charge $200 to make a profit. The current Atom chips are price competitive with ARM based alternatives. The Atom parts aren't quite up to par with an A15 based part yet but I think it'd be foolish to count Intel out.

The primary cost of a SoC is manufacturing. Process advantages mean that you have access to cheaper transistors that have better performance and power characteristics. The easiest way to improve the ratio of performance to anything in microprocessors has always been to make it smaller. There have been far too many words wasted on the role of instruction sets and architectures. Those things matter but that's the easy part. The hard part is getting a meaningful advantage in the manufacturing side, which is what Intel has. This is precisely why AMD is dying. They can't even undercut Intel because Global Foundries is so far behind Intel that they physically can't produce an equivalent product for less despite Intel's ~60% margins.

I think what you will see is Intel getting more aggressive in the mobile space in the next couple years because they are going to want to ensure that TSMC doesn't get a chance to catchup. TSMC is the real key to anyone threatening Intel not ARM.