Shrinking the picture simply makes it's details imperceptible to you.
If I may, can I suggest that this one sentence sums up some of the disagreement in this thread. DoF is, in fact, a concept
that is rooted in human visual perception. DoF is defined as the distance in front of and behind the plane of focus that appears
in focus to a human being. The calculation requires assumptions regarding human visual acuity, print size, and viewing distance.
I believe, others can correct me if I'm wrong, it is also implicitly assumed that the print size and resolution is such that the individual pixels in the print are too small for the viewer to see them at the assumed print size and viewing distance. If the pixels are visible then the entire image would not appear sharp. That is why sensor resolution does not appear in the calculation.
So yes, print size matters and yes, if you print small enough the entire image would "magically" appear sharp. "Appear" is the operative word in that statement but it is relevant because "appears sharp" is fundamental to the concept of DoF. If you also shrunk yourself down, your visual acuity would likely also change so in fact DoF would be the same.
And it is a concept. It is a defined value based on some reasonable assumptions. DoF is not something that exists independent of human vision and is not a strictly defined measurement like mass, distance, size, etc.
If you're looking for a physically defined parameter, it exists. That is focus distance. The distance from the image plane that is precisely in focus (in practical terms it would be maximally in focus because there is no perfect focus). And there is only one distance that is maximally in focus... every plane in front of and behind the focus plane is less focused. If human visual acuity was infinite and the resolution of a print was infinite you would be able to see the tiniest difference in sharpness. But that's not the case, more than just the exact plane of focus appears sharp and we can define the depth in the image that appears sharp... i.e. Depth of Field.