Sandboxes can have events and player goals, but the important thing is that the PCs are the drivers of what happens next. Having a story prepared tends to get in the way of that. In essence,
don’t prep plots, prep situations. As written,
Kingmaker has much more of the former than the latter.
I think it’s okay that traditional adventures can’t do every kind of structure. Structures are often tied to creative agendas, which have different (and sometimes incompatible) priorities. I think it would be fair to call
Kingmaker a hex crawl. I’d go so far as to say it’s sandbox-inspired, but I wouldn’t call it a sandbox. You’re not meant to play in it. You’re meant to experience the story it’s telling.
Consider the following: if the PCs decide that all they want to do is run Oleg’s trading post, would that ruin the AP? If it were a sandbox, no. It may have situations that occur on their timelines, but that’s just part of portraying a living world. The PCs aren’t expected to do anything. But
Kingmaker is about getting your own kingdom and using that as a vehicle for the story it wants to tell. A GM could roll with it by using the AP as a source for homebrew, but you’re well outside the scope of what it expects.
I should also note that Paizo has their own definition of sandbox, which they include in the GMG in the section on
adventure design. As they put it: “you give the players a sizable location to explore and let them decide how to go about it.” There’s an implicit expectation that the players are playing through the adventure’s plot, which they make more explicit in the section on
hexploration: “Even a sandbox adventure has a story or is the setting of multiple stories.” This is from PF2, but I think the ethos follows from PF1.
Let’s just say I don’t agree with their take on sandboxes. I don’t think it’s necessary to shoehorn everything into the traditional adventure structure, and I find it a bit exasperating how the traditional structure is taken to be the natural and default form of adventures.