Good question.

It is true that Google's Disaster Recovery Testing events are also about breaking things on purpose as a means of preparation. However, those events are typically large-scale, company-wide drills targeting not only critical systems but also business processes involving people.

(They even prevent experts from participating to make sure knowledge is spread across the organization. I recommend reading http://queue.acm.org/detail.cfm?id=2371516 for more.)

As dastbe has pointed out, Chaos Engineering is more about experimenting in a continuous, automated (and hopefully safe) way. Compared to DiRT, experiments are typically smaller in scope, involving fewer people, if any.