x86_64 is also known as AMD64, and for good reason. AMD created the core 64-bit x86 design, but, more importantly, they have patents to key pieces of the ISA required to legally implement it.
So, long story short, it is actually AMD who didn't have to share anything with Intel if they did not want to - Intel's 64-bit x86 CPUs are fundamentally AMD64-compatible CPUs.
The most interesting thing is it resulted in a bit of an interesting legal relationship between the two. Intel licenced AMD the required rights to produce x86-compatible processors. AMD, in turn, ended up licensing Intel the IP required for Intel to create x86_64 chips.
Sources:
https://en.m.wikipedia.org/wiki/X86-64#Licensing
https://www.sec.gov/Archives/edgar/data/2488/000119312509236...