For example, they ought to have the upper hand in the U.S. as long as the Chinese name more commonly refers to their game than the copycat's (since U.S. is not first-to-file), but it sounds like Apple is nevertheless prohibited from including their game under Chinese name in the U.S. (for Chinese-speaking U.S. players) due to PRC law.
No country use first-to-invent anymore.
It's a slim but important distinction, but it's not like copyright works. You don't get to register someone else's trademark because you wrote it down somewhere and kept it in the safe for 20y.
Though with unregistered marks you may not be able to stop someone else from using a mark they adopted independently after your first use. Trademarks are territorial, and classification based (registered marks are registered for a particular class of business; not relevant in the OP, but worth mentioning).