I can sort of understand the sentiment behind that, but the LPGA went about this totally the wrong way. These women should be encouraged to learn English, not singled out like this. It's not unreasonable to expect them to speak a little English, though: they're playing in the US, winning US money, and serving as faces for the league. Plus, it's just polite to be able to do more than smile and wave.
But, the line about how it's a sports entertainment world was crass. First of all, it's women's golf. Golf is a very popular sport played by Americans of both genders, but women's golf on TV isn't very popular. Men's golf, on the other hand, I'd say has surpassed the NHL in terms of popularity.
Secondly, I think they should be doing their best to get away from this "entertainment" talk. Look at the biggest name in women's golf, Michelle Wie. She doesn't participate in LPGA events because she stubbornly insists on trying to compete with the men, although she fails every time. And each time she opens her mouth---or her father speaks for her---she says something stupid. She's quickly become the Anna Kournikova of women's golf, and based off her example that's exactly why the LPGA shouldn't be trying to get more like her.
Finally, plenty of athletes in American leagues didn't speak English when they got here, but that didn't prevent them from becoming huge names. (Perhaps they'd be even more popular were they American, but that's another story). Ichiro Suzuki from baseball, Yao Ming from basketball, to name but two, and the countless Europeans in the NHL. From my own hometown, Mario Lemieux didnt' speak English when he came out of Quebec in 1984, but he went on to become one of the most popular sports figures in Pittsburgh. He eventually became fluent in English, became the face of the Pittsburgh Penguins, and went on to buy the team.
As for the "English Only" talk, I know the US doesn't have an official language, but I don't think it's unreasonable to expect people to make efforts to learn the language of their community. I'm not of the "Speak English or Get Out" camp, but, for example, I support the stance taken by the Philly cheesesteak owner who put up a sign telling his customers to order in English, although plenty of people were offended by that. Ask yourself if you'd be offended if Korean restaurants put up signs telling customers to order in Korean? Actually, that'd be expected. I cringe each time I see foreigners insisting on speaking English to clerks as if they understand.
Also worth mentioning that the Korean basketball, volleyball, and baseball leagues have quotas on the number of foreigners who can play on each team. If this LPGA story becomes news here, I wonder if people will call attention to the quotas in place here.