Around here, we're big fans of the motto "Hard is good." Playing a chess Grandmaster? Hard! You're pretty much destined to lose. I think I'd even say that to my child upfront--"You're going to lose. Know that right now. The goal of this game is to do the best you can BEFORE you lose. But you will lose, and that's okay."
I often tell my kids that if you don't make any mistakes, if you perform perfectly, then what you're doing is too easy for you.
FWIW, I think if I were you I'd sit down and discuss this with DS7 at a time when he's in a cheerful mood. That's given me better success with my kids than waiting until they're upset. Lay the foundation every chance you get so that when faced with adversity, he doesn't see it as a trauma.
I also battle my own perfectionism every day, I'm afraid. I know I'm not a very good model for them!

I do try to ease up on myself, however, and I do my best to make clear that I'm struggling with it, too.