This somewhat false, although it takes a lot of backend work to do it right, and it's not for fast paced action games. I'm working on rewriting an online game I had running a couple of years ago in C2, and it's working great.
Games that can live with Ajax calls as a primary means of playing can be done very easy in C2. Your C2 app becomes a UI container while the backend does all the work. It checks for updates from the server every x seconds, and when you click a button it sends that to the server for processing.
A battleship style game could be done in this way...but again it's beyond the scope of C2 itself to pull this off, as most of the game itself is being computed on the server in whatever language you're using there.