can we teach dogs to play chess?

What Dogs Can Be Taught
Owners have successfully trained dogs to participate in "chess" through high-level obedience: 
Piece Recognition: Dogs can be trained to distinguish between specific pieces by scent or sight and pick them up on command.
Executing "Moves": A dog can learn to move a piece from one square to another when cued by their owner.
Ending the Game: Some trainers have even taught dogs to bark after a specific move to simulate a "checkmate" announcement.
 
Cognitive Limitations
Abstract Reasoning: True chess requires understanding complex rules and anticipating an opponent's future responses, which is beyond a dog's mental processing.
Pattern Recognition: While dogs are excellent at recognizing immediate physical patterns, they cannot grasp the symbolic "power" or varying movement rules of different chess pieces.
 
Real-Life Examples
Bindi the Australian Cattle Dog
: Taught by her owner to pick up and drop pieces on a board to "compete" in matches.
Training Frameworks: Some specialized programs, like Success Dogs, provide step-by-step guides on how to teach these movements as a series of behavioral "milestones".  Success Dogs +2
Are you interested in how to train a dog to pick up and move a specific piece, or are you looking for simpler logic games designed for pets?
 
6 sites
How To Teach A Dog To Play Chess
Aug 16, 2014 — The fourth milestone is adding some extra pieces from which your dog must distinguish the right piece to pick up. You'll want to a... 
 
CHESS
Jan 16, 2025 — Dogs can't learn chess in the way humans do. Chess requires abstract thinking, pattern rocognition, and strategic planning, which ... 

Clever Pooch Plays Chess With Owner
Nov 16, 2022 — ID: 3528431 ONSCREEN CREDIT - @bindigordon2489 This dog owner taught her Australian cattle dog how to play a game of chess so they... 

do you think we can?

Yes we should

Like you said, yes we could teach dogs to "play chess" if you consider moving pieces aimlessly "playing", but predicting your opponents moves is pretty much impossible for them, i think it is going to be a huge progress even just teaching them that they need to move or protect their King in case of check.