Oh, and for the mobile phone market, there's Atom.
Are Intel licensing that to other manufacturers for SOC use? No? Then it's not a real player; cutting the component count at the overall device level is more important than speed to phone makers, as it's cheaper for them like that.
Intel sells full fledged SoCs equivalent to Samsung's Exynos line, etc. with Atom cores. Sure ARM licenses cores, but they aren't even a fabeless chip company they're a processor IP company. They sell Nvidia, Samsung, MediaTek etc. the right right to use ARM IP in their SoCs, which are then fabricated by TSMC, GlobalFoundries etc. Of course Intel isn't going to license you their cores. They want to sell you an SoC they designed, not their IP. That's like saying Qualcomm isn't a real player in the SoC business because they didn't license the Krait core to anyone else.
In addition, on a more general note, comparing margins from fabless guys to Intel is always a bit disingenuous. Intel, being vertically integrated, gets to combine the margins of the foundry, core IP house, EDA guys, and final SoC integrator. Of course they'll have better gross margins.