Intel licensed x86 to provide a credible second source, which they needed for some of their early business deals.

For AMD the primary driver was IBM.

In order to get the contract for the IBM PC, Intel had to agree to have a second-source manufacturer for their CPUs. Intel already had a relationship with AMD so it made sense to use them.

Patents, lots of patents. A lot of them are expired. By now you could make an 80486 and I guess also a Pentium clone without worrying about patents. But there can also be patents on how you make something performant on modern silicon, so it's not only about the ISA.