I define colonization as taking foregin populations and settling them into an area that is already part of a land claimed by an indigenous people, and then eventually displacing that indigenous population. Normally, there are economic, political, and military forces at work to foster the depopulation of the indigenous, or the removal thereof.

I don't disagree with the idea of a thousand people claiming all available living space, but we do have to accept that there is some limiting factor. If there was no UK government, I wouldn't consider it depopulated enough to re-settle people simply because it's not as dense as Shenzen. Some places do need to be recognized as part of an indigenous people's territorial claims (even to the point of highly mobile people), but, as you say, it can't be everything.

People invading and occupying already densely populated nations and leeching from them like parasites isn't the same thing.

It's precisely the same thing. Colonization isn't just in the form that the British Empire used.