Since there's a link to 'unvote' next to the option that I chose, I can only assume that this poll is not anonymous and that my choice is stored with my username somewhere on HN's server. It could also be cookie-based, but something to keep in mind if you have privacy concerns.
I imagine they could simply keep track of whether you voted or not, and not which specific choice you made. That way your choice remains private but we would not be able to show even you which choice you made.
I’m sure Reddit tracks each upvote and downvote individually and doesn’t just increment a score counter somewhere.