Nonsensical nihilism is just regular garden-variety nihilism with one of its attributes pulled out as an adjective to point out that this feature is the one I care about most.

Nihilism, philosophically, is the idea that we cannot know anything: nothing is justified to any extent, statements only appear to have meaning, etc.. As a positive statement that this-is-how-things-are it is, of course, self-refuting. But who cares? We just felt like saying that. Or we didn't. We just said it. Or not. Whatever. Really. Just. Whatever.

The spectre of nihilism was mostly clearly raised by Descartes by postulating an evil demon of limitless power whose sole task it was to confuse you. Thus he came up with his famous "I think therefore I am" counter to pry back at least one bit of knowledge from the dastardly demon. People have since pointed out that Descartes could, thanks to the demon, be so confused about every aspect of the statement that it's meaningless, so alas, the demon seems to have won.

Anyway, you can't get any sense out of nihilism.

Thus, nonsensical nihilism.