Yeah, that's what I remembered, but it seems they replaced "Delete Location History" with a "Manage Activities" button which opens Google Maps and shows you location history, allowing you to delete it but only one day at a time.
EDIT: Okay, found it. Follow your instructions then open that "Manage Activities" -> Menu -> Settings -> Scroll down -> Delete All Location History.
You _must_ do this for every account if you have multiple.
I guess it could be both but I view it first as a setting of the account since you can also be location tracked perhaps by a browser, or your Wear device? That would be my first go-to on that setting but I guess it can be seen both ways.
EDIT: Okay, found it. Follow your instructions then open that "Manage Activities" -> Menu -> Settings -> Scroll down -> Delete All Location History.
You _must_ do this for every account if you have multiple.