Thanks! So machine differences in their FP units drives the entropy, and the code doesn't handle that when picking eigenvectors?

It doesn't have to be their FP units; it could be that they run the operations in different orders, or that some different modes were set. I don't think the blog post goes into detail as to why but it does explain how this "cascades" into very different results coming out of the actual operation being performed.

Implementations of IEEE-754 can differ between machines, and the order of operations in a library/compiled function can also be different. It is not entropy, it is the nature of floating-point arithmetic.