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.
They could be doing this because the legal arm of their publisher wanted some form of affirmative defense, or they could be doing it because unhealthy players may not be around to buy the sequel, or they could be doing it because it seems like the right thing to do. It will vary, but it is almost always not a backhanded way of getting players to play more. There are far more effective tactics for doing so, such as Skinner box techniques.