That depends on how we look at what separates a Sport vs a "Game". If Sport is something that needs you to move a part of your body to execute it, then no board game or pure mental exercise is a sport. But if we look at Sport as something that you would work on to get better, actively, through learning, training, practice, then anything done at a top level is a Sport. Which is how I look at it.
If you play cards with your friends and never think of anything about what card you want to play, and just get better by accident through a lot of play, not through study, you are playing a card game. If you read 3 books on poker and enter $1,000 entry free tournaments and think about what cards to play when every 5 minutes in a day, then you elevate that card "Game" into a card "Sport".
That's my opinion on Sport vs Game.
Again, it matters not how well you do something. 5 year olds can play baseball, it's a sport whether they are good or not. Even 55 year olds that play baseball. It's a sport, and some just might sux at it.
Cards is card, and is never considered a sport. It requires ZERO hand-eye coordination, or anything else considered even the least bit athletic. I can play poker, on line, for money, from my sofa. Sorry, I'm not gong to the Olympics that way