A quick search for Engagement Manager roles,on Indeed shows about 12,000 live vacancies. A long way short of the 58,000 results for Marketing Manager roles, but a substantial number nevertheless for what is a relatively recent concept.
We used to talk abount customer "loyalty". "Engagement" is a far richer, more purposeful term. Some seem to be hedging their bets ("Marketing and Engagement Manager", "Loyalty and Engagement Manager"), but that smacks of tautology."
Marketing" has always been a bit of a portmanteau, blanket concept that covers pretty much everything a business does. Engagement covers the core of what I'd want a Marketing Manager to focus on - the customer's relationship to the product.
Is it the beginning of the end for the "Marketing Manager"?