I don't think people understand what you mean because they keep bringing up recreation, enjoyment, etc. while enjoyment is only a (possible) EFFECT. Reading is often an assigned chore and not a pass time. Some games are tedious.
Make an argument for the three things (watching, reading, playing) having a common denominator. Otherwise you can't be sure people understand you; and, also, in the course of doing so you may have a Eureka Moment.
Most likely you are charting new territory, it seems to me - even though to me and many what you say makes perfect sense.
"Taking in" or "experiencing" seem to be common denominators.
Since not many people understand the concept, I don't see how they'd understand the use of a common word.
Make up one from Greek roots, maybe? That would take explaining, though.
How about a descrptive phrase or multi-word term?
A metaphor might do the trick.