I really think you're conflating the (subjective) expression about an entity being a "major/minor player" with the factual claim of a company having a majority or minority marketshare. They're different, but you're treating them the same. Hence, confusion.

Major Player: an important and successful company, especially when compared with other, smaller companies in the same type of business or industry. Source https://dictionary.cambridge.org/dictionary/english/major-pl...

Ergo, the vast majority of people would agree that Apple is a "major player" in the phone industry despite having a "minority marketshare".

PS. There's nothing wrong with the point you're making, I'm only pointing out that its confusing to others because of the terminology you're using.