"because they would have lost" -> we don't know if this would indeed happen because words "app" and "store" are so generic... writing them capitalized does not change this much, because everything you write in a title is capitalized in English language...
If we're guessing, another reasonable guess is that they worked out a licensing deal so they wouldn't have to fight Amazon but they could still go after the next guy that tries it.
Companies also drop cases where winning is simply not worth the money. Owning an App Store trademark doesn’t seem be valuable in the way say iPad is because it’s not a separate product.
That’s not the test, Word is a trademark despite WordPerfect coming out several years earlier. Trademark law is kind of silly, but forcing every product to be called either a made up word or some long description wouldn’t be a net benefit.
