The word "WIDE" means "more than average" so the term "WIDELY PLAYED" means something that is played more than average therefore these games must be very popular. And popular games are played everywhere.

Here are some other examples using this construction: The concept of freedom is widely known throughout the world to mean "the ability to act, think, or speak without restriction". The current global warming trend is widely acknowledged by the the scientific community to be a result of human activities on the planet. Marriage equality has become widely accepted among the populace. The Eiffel Tower is widely considered France's most famous landmark.

The adjective is "widely-played". Yes, you're right in thinking it means the games are popular.