The original amd64 came out in 2003. Any patents on the original instruction set have long expired, and even more so for 32-bit x86.
I know for example that Berkley when thinking pre-RISC-V that they had a deal with Intel about using x86-64 for research. But they were not able to share the designs.
Are you sure, especially considering China?
I doubt there is any legal barrier, because there are a few existing projects with x86 cores on an FPGA, as well as some SoCs. Here's a 486: https://opencores.org/projects/ao486
As for opencores, yes you can design them, but do any companies making commercial products sell them?