Looked like a genuine apology to me. And if it weren’t genuine, presumably there would be evidence that he still held the views deemed objectionable, from later statements and activities of his. The very enemies who published the news of the first offense would no doubt gleefully supply evidence of newer offenses, if they had any. But there appears to be no such evidence.
If he has stopped talking and acting in the way he did before, and says he was wrong to act in that way, it seems vindictive to hold his past against him. I suspect that Harvard just doesn’t want any association with anyone who even in the past uttered politically incorrect views. I suspect it’s a “public image” thing.
Further, if Harvard has the right to decline admittance to someone who utters offensive views prior to entering Harvard, presumably it has the right to kick out someone who utters offensive views while at Harvard. So if the kid isn’t sincere, and repeats the offense after starting at Harvard, he could be kicked out then. Harvard could make a public statement of righteous indignation at that time. But in the meantime, why not give the kid a second chance?