I never even realized it wasn't a privacy feature or something until now, and thus, I'm posting this so that someone knowledgable about this sort of thing can maybe figure out why this is happening.
[19:38] RUPATUPA: If that doesn't work and you're using Mafia, you can check its chat logs.
[19:42] The Dictator: yes
[19:42] The Dictator: though, for private conversations, it seems to only log your side, dunno what's up with that
[19:44] bmaher: dictator, that sounds like a bug that i have never seen or heard about
[19:44] RUPATUPA: Mine appears to log both sides. And it gets my name capitalization wrong.
I did a little investigating after that, and it turns out I was wrong, it's not that it only logs one side of the conversation, it's that the conversations gets split between two different files: All my outgoing messages end up in [date]_the_dictator_<name>.html as expected. But all the incoming private messages that I get over the entire day all end up together in [date]_the_dictator_the_dictator.html, which is why I (originally) missed them.
Lost suggested it might have to do with the space in my username, and/or my account being new enough that I have never used the older chat.
Anyway, to illustrate:
Yes, even when sending a private message to myself, sending and receiving end up in two separate files, differentiated by the handling of that space, lol: