Do we just call all of statistics "AI" now? I fail to see how or why applying basic machine learning techniques for data analysis is "artificial intelligence". This idea that intellection is nothing more than pattern matching is silly and needs to die. Conceptual understanding entails more than just pattern matching.
Sentiment analysis may ultimately just be "statistics" but IMHO it goes way beyond what most people consider statistics, which is collecting, organizing, graphing data. Sentiment analysis draws conclusions from the data, assigning things like "level of negativity" and "level of positivity" among other things. It definitely feels like an artificial type of thing that humans do, so artificial intelligence seems like a reasonable category to me.