This generally isn't a reverse psychology tactic. The aim is actually to remind players how much time they've been spending in front of the screen and, in some cases, suggest that it might be time for a break.
This is because it can be unhealthy for a variety of reasons, to play games for extended periods of time, and the developers want to look out for their players.
There are far more effective techniques for getting people to play more. "You've been playing for..." reminders are generally somebody trying to do the right thing, or (from a more self-interested perspective) establish a defensive legal position, or to self-regulate in order to avoid the creation of actual, legal, regulations.