Earlier quoted context omitted.
I'm not sure there is a false dichotomy present there. You're either going to burn in hell or you're not. The downside of trying something to get out of that sentence is small and upside is big. It's terrible theology but it's decent logic.
I think it's a false dichotomy because there is more than two possible outcomes. At one end you have 'there is no god' in which case it doesn't matter, fine, but then at the other end there's more than just 'worship God' - there's also 'worship multiple Gods', or 'worship the devil', or endless other possibilities of worship, with no strong reason to pick any one of them. Unless I have misunderstood the Wager.
I think category A would be believing in Jesus and category B would be not believing in Jesus whatever that means to you.