"Getting involved in games" refers to the ability of some people to involve their entire daily life within the game, being totally unaware of situations in the real universe and exchanging reality for the game.
"Playing games" refers to the ability to play periodically, but not to involve your whole life in it. In this case, a person likes to play games, but is not absent from reality, nor does he substitute his real life for digital.
The author chose the phrase "engage games" to represent how games have taken the place of real life, and can leave a person completely involved and conditioned to it.
