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Engagement is merely the ability to, or the degree to which you are able to, maintain interaction with something (a system, a game, a fidget toy, whatever) over time. It has absolutely nothing to do with entertainment, although you can use entertainment as a means of achieving or increasing engagement. However, entertainment is hard. People are entertained by different things to different degrees, and respond to their entertainment in different ways. Engagement on the other hand is a fairly simple behavioural matter and that’s a whole field of science (which is mostly bollocks, to be fair, but its lessons can be very effective when applied at scale).
Source: I used to be a behavioural engineer, specifically a gamification specialist. Engagement was the oil I was employed to extract, and entertainment the excuse my field used to pretend what we were (and still are) doing isn’t just social manipulation at scale.
I’m sorry, but ‘crash when pressing Ctrl+C’ is a hilarious bug.