The nice catch was by you.... Pointing out that note in pink that I missed. I have spent the last 2 days trying to figure this out!!!! Thanks for your help.
https://7sage.com/lsat_explanations/lsat-16-section-1-game-1/
In this video around the 1:46 mark it appears JY is representing the relationship as a biconditional. I agree with your single conditional translation. The way I came up with S-->/Y i…