You are comparing apples to oranges. The sensor size plays a huge role in desired depth of field. While you can get a very shallow depth of field with a f/2.8 lens on your DSLR, it is not the same on the Mavic which by the way has a f/2.2 lens.
The tiny sensor size of the Mavic 1/2.3" plus the short focal length of 4.7mm would not cause any depth of field issues in Alan's photos. You will hit hyperfocal distance when you focus at something which is 2m away from you. Besides, his other photos also confirmed the problem.
You can check it out for yourself with an online depth of field calculator.
A Flexible Depth of Field Calculator
EDIT/ I did some testing and it turns out I was wrong about the distance, you do need to focus further away for everything to be in focus.