TL;DR: What makes AI is not if-then statements, but rather the automated reasoning that went into selecting those particular if-then statements.
You're focusing on the structure of the output rather than how the output was produced. Having if-then control flow statements is not sufficient to make a program "AI". AI aims to enable machines to solve problems which currently people are better at. Machine learning, a subset of AI, extracts useful patterns from data. A commonly cited example of expert systems is diagnostic medicine.
This begs a lot of questions like, "What does 'useful' mean?" If the problem we were addressing was finding cancer in medical images, "useful" might mean, "able to accurately identify cancer in images at or above the rate of a skilled human examiner." There's also questions about the amount of data needed, the quality of the data, etc. These are outside the scope of your question.
There are various AI/ML systems that produce models consisting of if-then states. Decision trees like C4.5 build a hierarchy of if-thens (and random forests combine many decision trees). Learning classifier systems (both Michigan and Pittsburgh varieties) come out of genetic algorithms and form similar collections of logic.