After reading the linked article, I don't believe Kobe thought that he was "wasting time" by doing things with his daughters rather than committing to an interview which, I'm sure, would have been less fulfilling than being with his daughters. (He gets to choose what's important, not someone else)
Some of this stoic stuff doesn't make sense to me.
I think one of the points of stoicism is that the time we spend with loved ones and on our various duties can be greatly enhanced by practicing introspection to comprehend the importance of living in the moment, to understand "how much was wasted in pointless grief, foolish joy, greedy desire, and social amusements." For example, this is from Meditations:
Let this be your stedfast purpose to act continually, in all affairs, as becomes a Roman, and a man, with true unaffected dignity, kindness of heart, freedom, and justice; and disentangle your soul from other solicitudes. You shall thus disentangle yourself, if you perform each action as if it were your last: without temerity, or any passionate aversion to what reason approves; with-out hypocrisy or selfishness, or freting at what providence appoints. You see how few these maxims are, to which, whoever adheres, may live a prosperous and divine life. If a man observe these things, the Gods require no more of him.
I believe the stoics are saying that if the heart is not clarified though introspection, it's possible that the the time spent with loved ones could be wasteful as it may draw you and others down into those pointless griefs, foolish joys, greedy desires, and social amusements.