Blue
Ravenous Bugblatter Beast of Traal
I disagree a bit with your definition of a campaign.
For me, if it's the same characters (or same party) under the same DM in the same consistent setting, it's a campaign; and I'm not even completely married to the "same characters" part of that and could maybe be talked out of it. Doesn't matter if what they do adventure-wise is completely episodic or disconnected in the fiction.
From the DMG (pg 25)
CREATING A CAMPAIGN
The world you create is the stage for the adventures you set in it. You don't have to give more thought to it than that. You can run adventures in an episodic format, with the characters as the only common element, and also weave themes throughout those adventures to build a greater saga of the characters' achievements in the world.
This looks like you need a setting, common characters, and recurring themes even if episodic.
But later it contradicts itself, under Continuing or Episodic Campaigns (pg 36), where each adventure can be completely self-contained without any reference back or forward, fitting your definition well.
I see where you are coming from, and the DMG does back you up. To me it doesn't feel like a campaign if there isn't something tying it together, but that may just be me. Your definition is good.