You can definitely put down being a chess instructor as work experience. You might want to mention being a master/your rating/a significant tournament you won.
I think there are many soft skills that are associated with chess, so you could definitely include those.
Beyond that, unless you're applying for a chess-specific position, I don't think many employers will care.
professional oach
My entire resume is chess, lol
My entire resume is chess, lol
professional oach
I never though of that. A professional oach. I will be sure to include that! 
Try to think what would impress you, if you were a Human Ressources ignorant in chess. And avoid drowning the good stuff in things they would not know what it is.
So, ratings? No. But are you FIDE rated? Yay! "International Chess competitor" you can write then. Otherwise, "USCF chess player" willdo. (They won't know the acronym, but it's an impressive acronym, they may google it.)
Won some titles, trophies or else? Try to think of which are looking better, and pick a convincing formulation, such as "Winnipeg U10 bronze medal 2009".
If you coached, then from what year to what year, and where.
etc.
You get the idea.
never through of that
You could include that you are the president of Baylor's chess club, helped manage the Club's Instagram, and helped form Baylor's first competitive chess team.
^^
Maybe something to do with management and administration if you run any large clubs...
As many have mentioned coaching is definitely relevant as well.
Not a cheater
Not a bot
Good sportsmanship
Doesn't cry when losing. Doesn't disconnect. Has good hygiene and smells good. Washes hands with soap and water after using bathroom
irrelevant
1. Professional coaching (time management, sales, working with people, etc.)
2. Competitive chess (USCF rating of XXXX, representing the top YY% of all tournament players)
3. Leadership in Baylor's chess team
It's meaningful.
^^