How would that help the Professional pool player, what does it mean the them, with the Olympics bei g only held every 4 years?
First, I am sure you were looking for a sponsor, probably not exactly the same thing that being part of Olympics games. It is not technically a "sponsor."
But, to this question. Every country would have to invest in advancing their top players within their country. Largely, this would mean to grow the sport with tournaments, training, and in some even gambling.
Also many countries would try to bring more attention to the sport in their own country, in order to attract young talent to take up the game. They would have to develop their talent base. This would also lead to more tournaments and larger purses.
Basically, the attention that comes with that stage would open opportunities for sponsorship.