AMD chipsets were not as successful in the marketplace because unsurprisingly the AMD-chipsets cost more than the Taiwanese ones, and motherboard vendors (who are almost all based in Taiwan) stuck with their existing vendors. The dual-socket AMD machines (K7-based) pretty much all had the 760MPX on it because I think only AMD had a multi-socket chipset that was reliable.
AMD also inhereted a lot of DEC engineers, so it was no surprise that K8-era their 'HyperTransport' was really 'Lighting Transport', developed at DEC.
Interestingly, Micron had also developed a chipset for AMD in this era but never released it.
nForce was also not re-licensed from ALI/ULI that I recall but I have far less insight here. nVidia at the time had a 'total system play' in mind so they were attempting to do GPU/audio/network/chipsets for AMD & Intel and got designed into original Xbox (x86-based). Jensen I think used NRE money from MSFT to fund a lot of the nVidia chipset work.