What I find interesting is that Intel engineers actually designed their own 64-bit extension, somewhere along the same lines as AMD64.
Intel's marketing department threw a fit, they didn't want the Pentium 4 competing with their flagship Itanium. Bob Colwell was directly ordered to remove the 64-bit functionality.
Which he kind of did, kind of didn't. The functionally was still there, but fused off when Netburst shipped.
If it wasn't for AMD beating them to market with AMD64, Intel would have probably eventually allowed their engineers to enable the 64-bit extension. And when it did come time to add AMD64 support to the Pentium 4 (later Prescott and Cedar Mill models) the existing 64-bit support probably made for a good starting point.
Bob Colwell talks about this (and some of the x86 team vs Itanium team drama) in his quora answer and followup comments: https://www.quora.com/How-was-AMD-able-to-beat-Intel-in-deli...
Around the time of K8 being released, I remember reading official intel roadmaps announced to normal people, and they essentially planned that for at least few more years if not more they will segment into increasingly consumer-only 32bit and IA-64 on the higher end