They both symbolize the mastermind lunar boss and his true nature which is human and the most dangerous/powerful weapon that trumps all superpowers the mind.

All else is theatricality.

Thread: Glass 2019 Movie Decoded.
-He doesn't look scary.
-Mm-hmm. That's what I said to my son,
but he says there's always two kinds.
There's the soldier villain
who fights the hero with his hands,
and then there's the real threat,
the brilliant and
evil archenemy
who fights the hero
with his mind.

At the end of dark phoenix lunar boss plays chess which symbolizes how he operates and why he is so hard to beat as he takes precautions for every possible move his victims might make.