The argument is not about Singapore. You're making the argument that it's not a good idea to have government-run public housing (presumably in Berlin/US/UK) because one government somewhere they did something bad through that they could have done even with private housing.

It's an anecdote for your argument. If the argument was "did Singapore discriminate against people through housing" it wouldn't be. If the argument is "should we have public housing [here]" then it's an anecdote. You'd have to show that this would happen in the place in question. If you want to make a general statement, you'd have to make that clear and make the case that in such countries landlords wouldn't discriminate against you for being LGBT (which they absolutely do).

I’m not making any argument about whether it’s a good idea to have government run public housing. I think you have me confused with another poster.

Your definition of ‘anecdote’ seems way off to me. We’re talking about an objectively verifiable data point. Just because it doesn’t fully confirm some argument that someone’s making doesn’t make it an anecdote. Check the dictionary definition.

Anecdotes are objectively verifiable data points. The key is that they are a single data point and can't be used to make a general argument because of that. It's a single interesting story about an event. That is a valid definition of "anecdote".

Housing discrimination against LGBT people in Singapore isn't a single story, it's government policy.

The definition of 'anecdote' has nothing to do with arguments. 'Anecdote' isn't a back formation from 'anecdotal argument'.