I can't say that I know exactly what those expectations are in the players McVay wants, but clearly neither Goff nor Akers met them. Doesn't mean in certain offenses under certain systems and coaches that it can't work. Clearly it is working for Goff in Detroit.
And I don't think it is "personality" per se as much as is it a player's make-up and approach to the game. Maybe his reaction and the way he holds himself. For instance, I doubt McVay would put up for a second with the "poor me" body language that Kyle Murray of Arizona regularly exhibits.
Goff is a conservative QB. He needs to play within himself and within the system and is NOT an improvisor. He can NOT make lemonade out of lemons. He does NOT have a gunslinger mentality nor the ability to pass off of different platforms and arm angles. He does NOT have a charisma or swagger about him that draws others to him.
Stafford has all those things. He is McVay's kind of QB, even with his propensity to throw untimely INTs. Goff wasn't. Simple as that.
As for Akers, clearly Akers lived permanently in McVay's doghouse. I just don't think that Akers was McVay's kind of RB....whatever that might be. But apparently Williams is, at least as far as "make-up" goes.
But I don't for a second think that personality clash or something of that sort had anything to do with it. There is no way you can be a HC if all your players must be of some particular kind of personality in order to be on the team.