From the question and comments, I believe the word the OP is asking for and means enjoying something more when being in the center of the happening is engagement.
According to Merriam-Webster, engagement means "a job or period of employment especially as a performer," or "emotional involvement or commitment."
A simpler word would be just involvement, which, according to Lexico, means "the fact or condition of being involved with or participating in something" or "emotional or personal association with someone."
This has nothing to do with being self-centered or egocentric. It means experiencing the event better when you are actively participating in it rather than just observing it.