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"Fight Like a Card Player" happens sometimes even when appropriate and deeply integrated into the story. Kingdom Hearts Chain of Memories is very, very "Fight Like a Card Player" but it makes sense as the characters recognize explicitly that they're in a card game or have been turned into cards and that's what the game is about. The Chain of Memories plot revolves around cards. People fight like a card player in Yu-Gi-Oh! as well but that's part of the story. I think this is a trope but the "having nothing to do with the story" part is trying to force two unrelated tropes Gameplay and Story Segregation and Fight Like a Card Player together. They aren't related.
Cards are mentioned in Co M, but not to the degree you are stating, and Yu Gi Oh does not have the elements of this trope. They explicitly play card games, not use cards for things unrelated to card games.
Who decides what is a trope and what isn't or what various tropes cover? If it were up to me, I'd say "Fight Like A Card Player" is a trope that covers anything that models combat with cards, and isn't necessarily related to "Gameplay and Story Segregation."
Are you new here? If you want a trope with that definition, make another trope that fits it. Go to YKTTW (but first read the YKTTW Guidelines), and then suggest it.
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How well does it match the trope?