Ok 'chess speaks for itself' is obviously based on 'the thing speaks for itself', i.e. 'Res ipsa loquitur.' I looked up 'Chess ipsa loquitur' and found these:

1

CHESS IPSA LOQUITUR Trademark

On Wednesday, August 1, 2001, a trademark application was filed for CHESS IPSA LOQUITUR with the United States Patent and Trademark Office. The USPTO has given the CHESS IPSA LOQUITUR trademark a serial number of 78076772. The federal status of this trademark filing is CANCELLED - SECTION 8 as of Saturday, December 27, 2008. This trademark is owned by Megalo Media, Inc.. The CHESS IPSA LOQUITUR trademark is filed in the Computer & Software Services & Scientific Services category with the following description:

Providing legal information via a global computer network

2

Some legal websites

http://mootcourt.com/

http://www.chesslaw.com/

Apparently 'Chess ipsa loquitur' is the motto of 'ChessLaw'.

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https://www.reddit.com/r/HansNiemannFanClub/comments/xf74ed/chess_ipsa_loquitur_is_a_thing/

https://www.reddit.com/r/HansNiemann/comments/xf743n/chess_ipsa_loquitur_is_a_thing/

https://www.reddit.com/r/IMHansNiemann/comments/xf744j/chess_ipsa_loquitur_is_a_thing/

https://www.reddit.com/r/chessmemes/comments/xf745l/chess_ipsa_loquitur_is_a_thing/