I don't know about Chinese chess, but in Western chess we have a long tradition of playing the game by correspondance. This kind of slow play by post or telegraph has existed since (at least) the early 19th century. Even some of the strongest players have enjoyed playing this way, for instance the first World Champion Wilhelm Steinitz. 

Turn-based play like we have on BrainKing is an extension of that tradition into the internet age. I'm guessing your real problem is that you're not used to seeing Chinese chess played this way. Get over it. That's how we like to do things here.