The idea of playing a game assumes the person is engaging in that activity by choice.
The only person engaged in the research here, I believe, who had not talked with me about it at one time or another.
On the other hand, a person can engage in sexual activity without an actual desire for it.
None the less, a person who gives reasons is engaging in a valuable activity.
Private persons may engage in education of all kinds and grades.
A person engaged in the selling and/or distribution of Cocaine.
When one person engages in voluntary trade with another, both are typically made better off.
Even if all of the above factors are present, the person will not engage in the behaviour without motivation.
You also want to have that person engage you in questions or discussion.
Each person engages in individual meditation or prayer even if others are present.