There was a recent thread in the news section which turned to this subject and a heated discussion followed.
In both cases the idea was raised by a Brazilian poster because (I believe) the matter is being discussed in
brazil. High profile sportsmen such as Neymar who play poker were asked the question and they were enthusiastic about the idea. First, I think poker is enjoying a high profile in Brazil not matched in other countries...and the country just hosted the Olympics recently...so the view is a little naive and perhaps Brazil-centric.
As others have pointed out, its is a mind game. Secondly many countries do not allow poker or gambling so it is hardly a global sport. But, more importantly as I pointed out in the other thread the Olympic Committee already looked closely at a card game which would have made a better fit with the Olympics - Bridge.
Whilst world class Bridge players can make a lot of money it is not regarded as a 'gambling' game as such but more a strategy game. Players compete in teams of two and there are long established world championship tournaments, It would seem to be a good potential fit for the Olympics. But the IOC rejected Bridge.
As I said before, if the Olympics already rejected Bridge I doubt they are going to seriously consider Poker as an Olympic 'sport' any time soon.