Simply put, the distinction between Statistics, ML and AI is not as straightforward as it may seem to those outside these fields. So if you're looking for a cut and dry definition to decide when something is ML, when it is AI or when it is Statistics, I'm afraid you're going to be disappointed.
With that said, the rather vague goal of AI is to create "human-like intelligence". This could include tasks such coming up with very advanced strategies for a game, voice interaction a la Siri, facial recognition or playing Jeopardy. In many cases, a machine learning/statistical model is used to make decisions under uncertainty, wrapped up in a whole lot more machinery to make the whole thing work.
Now, if one can just use standard if/then statements to write a program that appears to show "human-like intelligence", then there's no reason why we can't call this AI. In fact, one could say that something like a Random Forest is a very large pile of if/then statements, and this model could be used to make predictions under uncertainty for our AI agent.
On the other hand, if your if/then statements are so simple that we can fully understand what will happen, such as "turn up AC if heat is above 80F", most people wouldn't think of this as "intelligence" as much as a simple recipe.
Side Note: many of the statements made in the link provided are very questionable or just plain wrong. Here's a few:
ML is a subset of AI.
While the distinction between AI and ML is blurry, making such a strong claim that ML is a subset of AI is questionable.
ML refers to systems that can learn by themselves. Systems that get smarter and smarter over time without human intervention.
Again, there's no reason to think this is an official definition of ML.
Deep Learning (DL) is ML but applied to large data sets.
Deep learning is a specific method; Neural Networks with many layers.