The term is "presidential temperament".
John McCain didn't have it. He was thin-skinned...and mean.
Trump is expressing a similar lack. He can be thin-skinned...and petty.
Yes, and his behavior may work in the private sector. As it is, his contempt for everyone, his bragging, his bluster, and his name-calling will make it very difficult to build a team that cooperates with him. If Trump were to win, he’d have to have a one-party government filled with Trump’s chumps to get his agenda through. Like Obama, he demonizes everyone and then expects people to believe it’s all their fault. Childishness is not a leadership trait.