Someone with a product does NOT need permission to sell to players. Someone with a product that wants to advertise it on one of my web pages DOES need permission to post their ad on my page. Having a league or a web page does not give everyone with a product or service free reign to advertise on our personal or league web pages.
My apologies if I didn't make that clear in my first post.
As far as clearing it with APA first, if a product (not specifying any particular product) ends up being a big pile of junk and it was promoted through League Operators directly or indirectly by way of our web pages, we could all be standing there with egg on our faces. By going directly through the APA National Office, you might get support from them to promote it through all of our leagues, and they might even help you accomplish that goal if the product would improve your APA experience in some way.
As it stands, this particular product seems to only work with APA's 9 Ball 10 point scoring system. If the intent is to try to sell that product to all of APA's members, asking APA directly if you can have approval to do so would be the best avenue to take going forward. Getting their blessing gives you a much stronger platform to sell your product.