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
I never though of that. A professional oach. I will be sure to include 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.
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.
^^