Most likely the same, unless they are using some chip specific instructions/anomalies instead of just the published instruction set (which I think is unlikely).
There may be performance differences of course where AMDs chips process the same instructions differently internally, but I would expect similar optimisation differences between different families of Intel's chips too.
They wouldn't bother if it didn't work well enough on AMD CPUs because if it worked significantly badly or not at all then people other than Intel simply wouldn't use it. Of course they'll make no specific efforts to optimise it specifically for chip designs that aren't their own, but that is not the same thing.
The important thing here is that while Intel is driving this, the code must be landed in browsers, which are not owned by Intel. Those browsers are not going to ship code that only works on one type of hardware, or is weirdly unoptimized on some hardware.
Having dealt with cpuid, there were plenty of caveats with how AMD did things vs how Intel did things. I can totally see Intel first checking to see if it was Intel and then punting just due to complexity and testing. Keep in mind that this article mentions p4 and athlon, so Intel would have also have had to care about Cyrix and Transmeta as well, which were different as well.
