Ikigai is not equivalent to happiness.
(There is an excellent Ancient Greek word for happiness: εὐδαιμονία [eudaimonia], which has a complicated relationship with its cousin ἀρετή [arete, or excellence].)
Nor do I think ikigai is essential to happiness. There are plenty of examples of people who are living a life of ikigai who I doubt are truly happy, as I am sure there are people in deep, loving relationships—essentially happy— who aren’t in a career with ikigai.
But I do think to live with ikigai—a life of purpose—can certainly help in the pursuit of happiness.