How did they request Luigi's mansion 3 for speedrun.com, How do you request an upcoming game?

They didn't have to request it. Series moderators have the ability to create new games.

Also, from the Game Request Rules: [quote=Game Request Rules]In rare cases, requests for unreleased games may be accepted by well-known users and only at site staff discretion... Games will not be added prior to release for users who are not well-known.[/quote]