I think this flaw is even smaller than the issue of using Google statistics to infer transition probabilities. It's just a shitty proxy, at best.
At the end of the day, there's a lot of assumptions going into this analysis. I hope I didn't make it seem more serious than I meant it to be – it's really just a fun project and kind of a joke not to meant taken seriously.
That being said, I think the conclusions are at least "directionally" correct. They might be off by a factor of 2x or 5x or even 10x, but the stationary distribution exhibits an even bigger spread (multiple orders of magnitude) so I suspect the final ranking is still "roughly" correct (with a very liberal definition of "rough")