The comma is used correctly. It's the abuse of multiple and that causes your doubt. This is not entirely incorrect but considered poor style unless used specifically with impact on mind:
Mary found a candy under the tree, and a chocolate steps further, and a lollipop at feet of a bush, and a cookie by some flowers, and a caramel in the grass, and two peppermints by the path, and a few tootsie rolls along the path, and two candy canes upon the doors of a house of gingerbread.
Remove the redundant and-s and you lose the meaning, the sense of blundering travel from point to point - you just describe a set of gathered candies, not walking from one to another.
I think in the case attached the writer wanted to convey that all the elements are essential and none can be thought as "secondary", that's why the abuse of "and" which normal rules of grammar would require only to be placed before the last item.