Not hinting that at all. Government is not the source of funding for the national pool federations.
Most of that money originates at the International Olympic Committee (IOC) level, which has a solidarity budget of billions. For example, the United States National Olympic committee gets $650,000,000 from the IOC per four-year Olympic cycle. The National Olympic Committees of lesser countries like Poland, of course, get less. It is easily forgotten that both the World Confederation of Billiard Sports (WCBS) and its member the World Pool Association (WPA) exist under the IOC umbrella.
Each National Olympic committee determines how the money received from the IOC is allocated across the various IOC-recognized sports. Sports already enjoying Olympic inclusion, invariably, get some of that money.
Other sports, and pool is one of them, have earned World Games inclusion but not Olympic inclusion. Some of the National Olympic committees of the world will fund sports in this category, as such sports may gain Olympic inclusion in the future. Poland is one such country. The United States is not.
So, no, government and political philosophy and ideology are not relevant here.