He’s said that he’ll drop out, but why should he? How much does it really matter if he loses?
For narrative purposes, sure, it matters, especially given that Kasich has yet to win a primary contest and that the commentariat puts a lot of weight on candidates winning their home states. If he loses, the media, the Cruz and Trump campaigns (and Marco Rubio, if he survives, which he won’t), and many others will call on him to drop out.
But Kasich has been transparently playing for a brokered convention for a while—his refusal to attack Donald Trump speaks more of a willingness to make a deal than any New Age Prince of Light and Hope principle. While Rubio has played the expectations game well enough by making sure that nothing really mattered until today, Kasich has played it perfectly by making sure that nothing really matters ever. He’s just kind of there. No one knows why, but he’s there.
Kasich has been playing a long game since at least February and there’s no reason to start playing someone else’s game now. His game is putting his head down and staying in the race, no matter what.