I never got the impression that it was any kind of attempt to match iOS or "boost engagement". It's simply that the Mac App Store was brand new, and it was time to phase out DVDs as the primary distribution mechanism.
They did sell USB flash drives with 10.7, but it didn't make sense for that to be the primary distribution method.
OTA updates were delivered through System Preferences for many years before the App Store, not on DVDs.
Sure, but I get my OS upgrades from the System Settings app now, what was stopping me from doing that in the early 2010s?
And yes, the Mac App Store was brand new, what better way to boost engagement than to move a fairly standard and typical function into it even though it was unrelated? Sounds like a good way to trick people into using your new thing. Like a boost, to engagement, one could say.