Tiddly-winks is more of a sport than baseball (or rounders as we Brits call it).
Why do they call it Great Britain?
The first World Series (1903) between the Boston Red Sox and Pittsburgh Pirates was sponsored by a newspaper called The World and the name stuck.
There are two major league teams in Canada (well, Montreal is arguably AAA but it plays in the majors), and one of them, Toronto, has won a World Series.
Further, anyone good enough plays regardless of nationality. The Dominicans (Sammy Sosa) are legendary. The Cubans (Tony Oliva) have put out their share of marquee players. The Mexicans have their own league near major league calibre. The Japanese support two. Korea has a pro league. All have sent players to the majors. Taiwan's greatest player could've played in the majors if he had wanted to-- Saduharu Oh, who now manages in Japan.
Europe has even given the great sport a few marquee players. The contributions of the English in founding the game are mentioned in other posts on this thread. The Netherlands gave us Bert Blylyven. In the early days of the game, there were so many Germans, Scotsmen, Irish and Italians that football was considered more of an American game by some.
Prior to the Ardennes offensive, the nazis attempted to infiltrate their soldiers behind American lines in such numbers that baseball lore became one of the main tools to sort out the imposters. The krauts had learned to speak English with an American accent, learned Brooklyn coloquialisms, even learned how to roll Bull Durham stogies with one hand. But when they couldn't reply who had played in the 1944 Series, what Lou Gerhig's last speech was or where Ted Williams and Stan Musial were stationed, they ended up in the stockade.