What's the word for Unnecessary Complexity

single-word-requests

Your particular example is not only overly complicated, but especially confusing as a result. I would therefore use convoluted:

1 (Especially of an argument, story, or sentence) extremely complex and difficult to follow —Oxford Dictionaries

Edited to add:

Note that the word's original meaning is literally "twisted" or "coiled", but it is now commonly used (at least in the US) metaphorically to mean confusingly complicated, as attested in the Oxford definition.

I think the connotation of twisting back on itself is quite useful here. Not only does the double negative cause a "reversal" in meaning, but it is likely to make the reader go back and re-read the end of the sentence so that the reader's eyes trace a Z-shaped path across the sentence: it is both figuratively and physically contorted.

A similar word is tortuous, which also has its roots in physical twists and turns (compare contort) but which is now often used figuratively. I'm more reluctant to recommend tortuous as I think it's easily confused with either torturous or tortious, but it would otherwise also work here.

As @Jim said in comments, the obvious word seems to be overcomplicated

ODO: