Not saying that the solution doesn't provide a valuable framework for building robust applications that can overcome those issues (necessarily pushing some of that complexity up the stack to the application developer), but the marketing seems a little bit suspicious?
Edited to add: In fairness, the article doesn't actually claim to have evaded CAP - it recognizes that HAT is a compromise. But I believe it's easy to understate the practical problems with non-serializable transactions. It becomes impossible to prevent duplicate transactions from being created on the split-brain nodes. In banking, for instance, this would be a Bad Thing, and lead to potentially hairy application-specific mop up when the nodes resync.