This is a fascinating summary of training process and accomplished results. Author is speech therapist for children and applies similar approach instead of rewarding dog for just pressing buttons. Most of comments here are too dismissive of methods and results.
I would argue this training is not about teaching the dog to communicate, they already do that. This is teaching the dog to communicate in a way that is understandable and verifiable to people other than their owner.
My dog learned to cough to get my attention and then point to the thing he wanted, or give me a look he knew I would understand. Barking at me would often just get my frustration, but he was so excited when he found out that we could both make the same noise coughing. After that, he would only bark if he was mad. Communication, but not with repeatable, verifiable 'words'.
There are enough that still explicitly do and another set that uses things like Evo Psych, IQ testing, and renewed interest in Non-African human origin and arguments that humans aren't a single species (since species isn't an exact term to begin with) to imply the same.
"Using a substantial number of trials, Pfungst found that the horse could get the correct answer even if von Osten himself did not ask the questions, ruling out the possibility of fraud. However, the horse gave the right answer only when the questioner knew what the answer was and the horse could see the questioner. He observed that when von Osten knew the answers to the questions, Hans got 89 percent of the answers correct, but when von Osten did not know the answers to the questions, Hans answered only six percent of the questions correctly."
Still pretty amazing capabilities, actually indicating advanced communication skills.