Start with an image with only two colors, then it will be easy to select background and continents with the wand.
Try the rendering filter cloud in black and red for the continents, and in yellow /orange colors for the background.
Edit the background with various filters like blur, noise, twirl, as you like.
Make a new layer above of all layers and fill with an artistic paper structure in multiply mode.
And so on ...
You will never get exactly the same result, but you will have fun.
The dirty/hazy edges look can be accomplished by Filter - Blur - Gaussian Blur then Edit - Fade - Darken.