The atmospheric pressure mat is approximately 10.5 x 10.5 inches and it does not let air under it when pulled straight up because of a tight seal between the rubber and surface.
There is approximately 1620 lbs of pressure pushing it down from the air mass above it and as long as no additional air can get under the mat it can theoretically lift that much pressure. In reality, it’s much less because of the imperfect seal between the mat and object and the small quantity of air under the hook.
As you pull up on the hook, the small quantity of air under it has a greater volume (gasses expand) and that creates a low pressure compared to the high pressure above it. This allows the mat and object it is lifting (which still has air pushing it up under it) accelerate up together when you lift the mat by the hook.
If you lift the mat by the corner air can get under it and push up as well as the air pushing down and therefore lifts easily.