There is no such thing as most important class in TF2, simply because a team can do just as fine without a certain class. Yes, engis are good defenders, but demomen, heavies or other classes could do fine.
If there would be a most important class, it'd be the medic... No offense needs a medic (except for the usual dustbowl pub sentryfest) but it's always nicer to have a medic than a scout who is just dieing nonstop. (I am not saying that scouts are useless, just saying that a DIEING scout is not as helpful as a healing medic).
Other than that, this is a pretty basic video. Though I can't agree with you about your "offensive" engi style. What difference does it make when you just use a different spot but still babysit your sentry like you'd usually do anyway? Exactly, none. It's just defending a different area.
-Calle