What's the technical aspect missing? Do you mean how many countries need to be represented before you can claim "from around the world" status? Or how many different games need to be selected? Or how spread out over the world the countries have to be?
(I agree that if you chose soccer from 50 countries, "games from around the world" would be misleading. If you chose 15 games from countries all in Europe, the phrase would also be misleading. Is that what you mean?
If you had protection rackets from Russia, political corruption from India, and womanising from France, the term might also be controversial.
What do you actually have?