A typical vendor-sponsered research result :-)
They never directly compared the Linux-based web-facing computers.
The original article at NetCraft is slightly more clear about this: http://news.netcraft.com/archives/2014/02/26/microsoft-neck-...
It appears to use number of domains as the measurement, not sure if sub-domains are included in that, but either way, is there reason to believe that Microsoft is running considerably more domains than Amazon? Sure they have more products, but not thousands more.
Therefore, I think it is safe to assume that most of these 'web facing computers' are customer servers, and if so, that is a telling sign for Azure. AWS has been in the marketplace longer, and has the mindshare. I'm surprised to see Microsoft anywhere near AWS numbers.