Final answer:
The fallacy in Nietzsche's critique is an Ad Hominem fallacy, as it attacks theists rather than the concept of God itself.
Step-by-step explanation:
The fallacy shown in Nietzsche's critique, where theists are claimed to be weak and invent the idea of God out of resentment and longing for comfort, leading to the conclusion that therefore God doesn't exist, is an example of an Ad Hominem fallacy. This type of fallacy occurs when the argument attacks a person or a group of people directly instead of addressing the actual argument or the evidence. Thus, it involves making a negative statement about theists to reject the existence of God without engaging with theological arguments.