I don't think you've quite got it, Fledermaus!
The part about the beer and the drinking is irrelevant - they're just there to set the stage. The important part for the joke is that Descartes says "I think not". His famous quotation is "I am thinking and therefore I exist", so the joke is that if he is not thinking ("I think not"), then he does not exist.
It's not really a joke that can stand up to too much analysis, I'm discovering!