Natural language processing is a big area where classical AI is heavily used and machine learning is lagging behind. ML is terrible at teaching computers to read and/or produce human writing. Compare what the company Automated Insights is doing for news articles versus neural networks writing books and movie scripts (with humorous results).

Anything with a known and well-defined set of rules can also be programmed more efficiently with decision trees/Markov chain than through machine learning. There's no need to use tons of data to train a model to do something over time when all it needs is the rule book.

Machine learning is basically advanced pattern matching, neural nets often require you to brute force the problem with tons of data. There are plenty of places where you're not matching patterns and you don't have tons of data but the computer still needs to make a decision after analyzing the data that is available.