So we learn a little about Mina's mom's past. But what is a moderator? And I doubt Mina's mom was a moderator post-Ending so this is something pre-Ending.
And more hints about Saisuke. Whoever he is, I'm betting we will find out and I don't think it will be pretty. It doesn't seem like Kleya is searching for someone (unlike him) and in fact she doesn't want to be found. She just wants to use the Game so that she can be seen as a good person and be allowed back in society. And I don't think Saisuke is looking for her. Because why would he be looking for some in the Game? Why not look inside of LiFe (since very few people make it to the Game). I'm also not sure if he is actually looking for someone because of the same reason. Searching for someone in the Game is not the most optimal way of doing it.
It could be that he's searching in The Game, in LiFe, and in Reality, all at the same time.
I think a more likely explanation is that he, at first, was looking for someone and couldn't find her. He became popular with the fans because of that quest (after all, who doesn't like watching a Star on his soul-searching journeys for a lost love?) and continued to 'search' for her in order to keep the fans.
Also, possibly, if he really is looking for Kleya, then it would be because he knows she'll come back to The Game if she's still alive. Maybe they were rivals pre-Ending.
About what a moderator is, I have no idea. Someone who moderates. Maybe it's the person in charge of announcing on that player's Channel to all the watching fans? Sort-of like a sports announcer, but with The Game.