That article reads incredibly presumptuously.
Here's his Holiness' facebook pagehttp://www.facebook.com/DalaiLama
I've no idea what the quote has to do with Harris. I kinda doubt the Dalai Lama is rejecting spirituality, nor even modifying his view of it, rather, more likely, he is seeking ways to export it, not unlike students of Kabbalah have been doing since Madonna, nor New Agers since Castaneda
You really can't take the Dalai Lama out of context; he chooses his wording carefully. I've heard him speak; he's a very smart guy. He says "the time has come to find a way of thinking about spirituality
and ethics beyond religion
And this is obviously necessary in order for more people to access the message of religion. The guy is not abdicating the role of religion, he's advancing it. That's sort of his job. And there's no reason for him to do otherwise. There's lots of good information in there. The problem is wading through all the ceremony to get to it.
For instance. the so-called Tibetan Book of the Dead speaks of encountering hideous gods drinking blood out of skulls, among other fun, planned events. Oh really? So the nonreligious message in "thinking about spirituality...beyond religion" might be that yer gonna need some courage to face your fears. Oh, well, but that's not very religious at all. So you can apply that to ethical aspects as well.
Now, besides heading up one of the world's great religions, he is also a man of science and has been involved for years with a group of scientists and physicians in the study of consciousness. So it's not as if he's giving up one for the other. I've never heard Harris in person but I can tell you, the Dalai Lama is no Sam.
For millennia, the Tibetans have done a wonderful job of exploring what western science is just beginning to study. They have much to offer but so much is hidden in religion. Once they decloak to fire, they will raise their shields.
You might also find these guys interesting http://www.mindscience.org