The NYT article is weirdly written. It sounds like the writer has no idea who Neil Diamond is. The reason he's getting a musical is not because he's a successful songwriter or because he won a Grammy for Jonathan Livingston Seagull. He's been incredibly commercially successful as an artist with a lot of songs that have stood the test of time. I would argue that he's only a successful songwriter because he's written his own hits. He wrote "I'm a Believer" and others back in the 1960s but I think the only song he's written that's been commercially successful since then that he didn't perform himself was "Red Red Wine."
I wouldn't call Mariah Carey one of the most successful songwriters of the rock era as the lead in a piece about her, even though it's true objectively. But it's only true because she's written her own hits. I don't think she's written successful songs for other people. Someone like Carole King or Ed Sheeran can have that as the first sentence in their article.