Sport is more than just a physical thing
Yes, I believe that poker is a sport. Sport is not a simple physical thing. It's more than that. Sports is about skills training and continuos practices. You need to be patient and master some or all parts of the game.
Also, poker reports benefits, as happines, fun, mental training, emotional management. Just because you have not to run, it doesn't mean that poker no requires discipline, strategy, skill, practice, and mental endurance and strength.
If you think that poker it's not a sport, then, it's because you have a poor definition of what sports is.