It is supposed to be over the top. The joke in comic is that he used such a sensitive and controversial subject to build up to a stupid punchline that really isn't that funny.
The strip, however, is funny because the strip itself is the joke. There really is no punchline that would justify using the holocaust as a setup. If the setup and punchline was to be taken seriously, the strip would just be an edgy holocaust joke that would only be funny to /pol/ and the like.
The punchline and setup in this case is reversed. You read the beginning of the strip wondering what could justify this style and depiction of the holocaust, and then reach the "punchline." The gas bill and suicide itself isn't funny, but it contextualizes the strip. Now the bill and suicide "punchline" sets up the re-contextualization of the holocaust "setup" which is itself the punchline. Now the reader of the strip experiences a relief of the tension because previously he or she had been expecting an edgy holocaust joke, but instead the joke is that holocaust jokes aren't funny. The reader is relieved. Laughs