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.
It's false in the sense that it only provides two options and seems to indicate those are the only two options. Believe in the Christian God or don't. It doesn't take in to account Jupiter or Zeus or any other potential deities in determining the 'logic' of choosing to believe or not.
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.
I think the assumption is that you are considering believing in a Christian God and on those terms the wager is valid. As far as I know other religions offer little promises in terms of what happens if you stick with it.
I think category A would be believing in Jesus and category B would be not believing in Jesus whatever that means to you.
