Chinese Chess
Probably because it doesn't exist. I've only heard of chinese chess. What's chines? 🤷♂️
Chinese, genius...I inadvertently omitted the "e" when typing my post; flaw of typing too fast. You get a gold star, Punctuation Punk...!!!...
The name in Chinese.
象棋
Elephant Game.
象
is a glyph of an elephant. 4 legs, 1 tail, 2 big ears, and a trunk.
It is named Elephant to commemorate its Indian origin.
Elephant Game is the most perfect name for Chess.
Charlemagne Chess Set. Bishop (Elephant).

I just saw the movie Napoleon last night with a Vietnamese lady friend and her American husband.
I gave her my Caesar and Napoleon Chess set (a splice of 2 sets), and a Chinese Chess set.
When Talleyrand appeared on screen, I said, "He's the Bishop." to the husband. He transmitted to her.
I was thinking, does she understand "bishop"?
I told her in Vietnamese, "Con tượng." The elephant. I calque it correctly too from the Chinese. If I were to calque from French I would say "the canine" and not "the dog'.
She said, "Oh, ok". She understood,
When in doubt, go back to the root word.
https://www.chess.com/forum/view/chess-equipment/luxury-chess-set-1?page=2#comment-92571179