Do Intel processors/chipsets have their own LAN chips now?
Solution 1:
You are looking at the chipset rather than the actual processor. The chipset is the Platform Controller Hub (PCH) through which the processor talks to SATA disks, PCI and PCIe devices and a multitude of other things.
Intel have long had their own line of ethernet chips and controllers, integrating one into the PCH is not surprising at all. I personally have worked on projects with the Intel i210 ethernet controller.
So yes. Your motherboard can have integrated LAN built into the motherboard controller.
But no. It is not built in to the processor.