I think those those numbers came from this pdf in 2007 -
https://www.fifa.com/mm/document/fifafacts/bcoffsurv/emaga_9384_10704.pdf There are (were) some interesting things to take out of that.
Like you said, percentage wise there were less players there than in other countries per head of population. They only list the top 10 and it was mostly small countries without much football pedigree although Germany and Chile were doing excellently.
There were around 2/3rds the number of female registered players as there were male, which is unlike any other country. If they'd have had the same number of females playing that do, and then the same number of male players in proportion that Germany had, they'd be on over 10 million male players instead of 2.5m. Not that there's anything wrong with having a lot of female players, in fact it's good! Different split though, and we are talking about men's football primarily in this thread.
Football appears to be a kids thing in the US compared to elsewhere.
3.9m youth players out of 4.2m total players leaves only 300,00 adults. Whereas Germany was 6.3m registered, 2.1 youth leaving 4.2m adults. France was 1.8m registered, 1m youth and 800k adults. England 1.5m total, 820k youth, 780k adults. It is ultimately adults who participate in World Cups etc. If they don't play then that's your talent pool reduced. Plus seeing as a lot of their youth were female compared to elsewhere maybe there adult leagues are too?
Elsewhere it looks like participation levels dropped in kids football between 2015-18, when this article was written -
https://www.nytimes.com/2018/07/14/sports/world-cup/soccer-youth-decline.html[/spoiler]