If there is no feasable way to contact a game moderator through means like discord, twitch etc. would I make a thread about requesting the game to be added or would I make a forum post asking a game mod about the game(s) in question?

You can try making a thread, but if the thread gets no response and the moderator remains inactive, you can request to become a moderator of the game here https://www.speedrun.com/The_Site/thread/63nr7

If a mod is inactive, has no social media links and isn't responding to requests like that, it's a pretty good case for becoming mod yourself. Just make sure to read the OP in that thread to make sure you and your situation meet the requirements.

Thats great, thanks to both of you for the advice ^^

My suggestion is that if they have a Discord for the community use that, else maybe try and post in the games forums to ask them to start one as It's a very useful thing to have to keep a community connected and growing.

Trust me I was told this by many people =p