Seriously what are they and where do I apply?

https://www.speedrun.com/requestgame?series=

Ways you can get moderator:

1 - Getting a game you requested on the site. If a request is accepted you'll become the moderator for said game.
https://speedrun.com/requestgame
2 - Getting added as a moderator to an existing game by an existing super moderator/site moderator. If the moderator(s) for a game are inactive/have not verified your run within 21 days/not existent, you can request to become a moderator for said game via the moderation request form.
https://www.speedrun.com/knowledgebase/supporthub/request-moderation

The requirements to moderate a game can be seen in the moderation rules.
https://www.speedrun.com/knowledgebase/moderation-rules