He owns more than 50% of the voting stock. Boards don't operate on one-man-one-vote, they operate on one-share-one-vote. If he had really wanted to stay no matter the consequences, he could simply have voted against his own firing.
That's not usually the case. Boards normally operate on one-person-one-vote. A majority of the current sitting board members can therefore fire the CEO.
Shareholder meetings operate on one-(voting)-share-one-vote, so a majority shareholder ultimately controls the composition of the board. But if one of "his" directors, who his shares elected, breaks ranks and votes to fire him, simply owning the shares doesn't allow him to immediately override that vote. Kalanick could have voted out the board members opposed to him at the next shareholder meeting, and voted in sympathetic ones, who then might rehire him as CEO. But that's a different question than whether he could win any board vote simply by virtue of owning a majority of voting shares. Shares don't directly have board votes, they just elect directors who have board votes, who usually vote with the interests of the shares that elected them, but might not always. Besides exercising their personal judgment, directors also have independent legal responsibilities that may in some cases make it prudent for them to vote to fire even the person who put them on the board.
