This is what the site says:

"StatCounter is a web analytics service. As of 1 June 2010, our tracking code is installed on more than 3 million sites globally. (These sites cover various activities and geographic locations.) Every month, we record billions of hits to these sites. For each hit, we analyse the browser/operating system used and we establish if the hit is from a mobile device. For our search engine stats, we analyze every hit referred by a search engine. For our social media stats, we analyze every hit referred by a social media site. We summarize all this data and this is how we get our Global Stats information.

We do not manipulate the data in any way. We do not collate it with any other information sources. No artificial weightings are used. We simply publish the data as we record it.

In other words we calculate our Global Stats on the basis of more than 15 billion hits per month, by people from all over the world onto our 3 million+ member sites."

The only thing they talk about are hits, and they mention it extensively. Maybe they do some analysis to determine unique users, but if so they don't mention it, and that would seem to be a pretty big oversight. That's why I said as best I can tell they use page hits.

UPDATE: I went to the Wikipedia link you provided and it says this: "StatCounter (July 2008 to present) Usage share of web browsers according to Stat Counter. Statcounter statistics are directly derived from hits (not unique visitors) from 3 million sites using Statcounter totalling more than 15 billion hits per month.[22] No artificial weightings are used"

This seems consistent with what I said earlier.

Speaking of...does wikipedia list their web traffic numbers? It seems like they would have a pretty good representation of the public knocking on their door.