Perhaps the difference is due to the fact that East Asians domesticated different kinds of cereal crops than Europeans did. Perhaps milk wasn't as important in a rice-based diet as it was in a wheat-based diet? (But then again, Indians eat rice and they're lactose tolerant according to the article.)

Or perhaps East Asians developed different kinds of social and economic structures that mitigated the disadvantage of not being able to consume milk.

Or perhaps the necessary mutations just didn't get incorporated into East Asian genes. Also according to the article, the lactose tolerance gene spread as far as India but didn't cross the Himalayas.