Everyone applying to Oxford is going to have top-notch grades. The interview would be pointless if it was based on that.
The interviews, like a job interview in some cases, are to get a feel for ther person that you are, see if you are suited to the kind of pressures that you'd be under at Oxford and to study your academic potential. Indeed, in the 1-on-1 tutorial system, the tutors interviewing you need to be convinced that you're someone they can work with and help.
I *speculate* that he may have come across as rather arrogant and the tutors may have disliked - indeed that he went to the Press to complain about the rejection may have proved the point. Oxford and Cambridge will always say "We had many exceptional applicants", as in this article, since it is less controversial than rejecting him based on more subjective criteria.
The article talks of his applications to the US as if there is some sort of equivalence in admissions considerations. Although top US universities do conduct interviews, they tend to happen when they're undecided about a candidate. They are more grade orientated. They don't rigorously interview everyone as Oxbridge does, nor do they have a similar tutorial system that necessitates it. Oxbridge candidates tend to have two or three interviews and even on the spot tests during interviews. Entry criteria are also very high, but they are not the same.