Why do some sources say women make up ~50% of gamers?

And then they vaguely detail their definition of gamer? To me I wouldn't call people who occasionally play games on their mobile phones to be gamers.

I think a much more accurate snapshot of the demographics is seen within GameSpot's About page:

http://www.gamespot.com/misc/aboutus.html

96% of real gamers are male. The ones that know about the major platforms, titles, read previews/reviews, watch trailers, etc.