I completely get what you're saying. Lyrics like
"Well thank you genius, you think it'll be a challenge
Only my life's work hanging in the fucking balance"
may seem that he's only concerned about his career and not about the loss of Chester.
But if we think deeper… if we think that as soon as he accepted that his friend passed, what's left for him? His whole life's work.
He couldn't do anything for Chester, but his work was still "in the fucking balance". He couldn't neglect it and it was killing him.
That's my reading about the theme. I was completely wrong on my reading about What The Words Meant, so I can be totally wrong here too.
Overall I think that the whole point of Post Traumatic, starting from the album's title, is that Mike wanted to talk about his grief, what he felt, his concerns, how he overcome it, and not about Chester or his — undeniable — friendship with Chester.
And we have to thank him for doing it. He could have followed the path of the other band members and kept his grief for himself, but he decided to share it with us.