Firstly I would say Nietzsche's writings show a deep ambivalence toward the Gods .. The introduction to The Birth of Tragedy, for example, which Nietzsche wrote years after its first publication talks about the "offensively Hegelian" character of his initial formulation of the 'opposition' between Apollo and Dionysus, taken together assuming the form of an "irrisponsible God"; the chaotic, suffering unity whose redemption is found in individuation, illusion, limit, masks, the 'dream work' of Apollo, with a synthesis of the two reaching a crescendo in Attic tragedy. I note this only as a single small example, and to point out that Nietzsche's work contains a world more than is ordinarily attributed to him in relation to his attitude toward God, the term encompasses a lot more in his work than his views on the Christian God. Off the top of my head, and just in brief, see aphorism 150 from Beyond Good and Evil, which Heidegger takes as the "guiding thought" of his second book on Nietzsche:
Everything in the hero's sphere turns to tragedy; everything in the
demi-god's sphere turns to satyr-play; and everything in God's sphere
turns to ... to what? "world" perhaps?
.. Having said that, the quote you cite is clearly satirical. One of the main things which Nietzsche's work emphasises is that the conditions of life also include error. Deleuze has a beautiful phrase in his Nietzsche and philosophy - "the affirmative power of falsity" ..
In your quote he is ridiculing attempts to disprove God because, as @Joseph Weissman notes to him the death of God, among other things, implies the absence of any transcendent guarantor of truth. The logic is egregiously unsound, as is the assumption that logic can be used to prove such a thing. For a comparison reason for Descartes was "the natural light", a divinely endowed capacity to perceive truth. Nietzsche did not believe this. One passage which illustrates his attitude toward reason is aphorism 11 from Human, all too Human
Language as putative science. -
The significance of language for the evolution of culture lies in
this, that mankind set up in language a separate world beside the
other world, a place it took to be so firmly set that, standing upon
it, it could lift the rest of the world off its hinges and make itself
master of it. To the extent that man has for long ages believed in the
concepts and names of things as in aeternae veritates he has
appropriated to himself that pride by which he raised himself above
the animal: he really thought that in language he possessed knowledge
of the world. The sculptor of language was not so modest as to believe
that he was only giving things designations, he conceived rather that
with words he was expressing supreame knowledge of things; language
is, in fact, the first stage of occupation with science. Here, too, it
is the belief that the truth has been found out of which the mightiest
sources of energy have flowed. A great deal later - only now - it
dawns on men that in their belief in language they have propagated a
tremendous error. Happily, it is too late for the evolution of reason,
which depends on this belief, to be put back. - Logic too depends on
presuppositions with which nothing in the real world corresponds, for
example on the presupposition that there are identical things, that
the same thing is identical at different points of time: but this
science came into existence through the opposite belief (that such
conditions do obtain in the real world). It is the same with
mathematics, which would certainly not have come into existence if one
had known from the beginning that there was in nature no exactly
straight line, no real circle, no absolute magnitude.