Yes, that’s Tim Cook narrating. As Rene Ritchie notes:
My best guess as to why Tim Cook narrated the “Better” video is because it speaks to Apple’s core values, and speaking to Apple’s core values is both deeply important to Tim Cook, and how he’s been positioned atop and within Apple.
You can say Tim Cook is not a product guy, but there’s no question that he knows better than anyone how Apple does what it does. And because he cares about it, he’s made that process… better.
This feels like the point where Tim Cook finally drew the line in the sand and showed what Apple looks like under his image. He’s been moving in this direction for a while, but unlike prior efforts, this doesn’t feel like Steve Jobs’ Apple under new ownership. This has Cook’s fingerprints all over it. More power to him.