An article on the topic, https://opensourceconnections.com/blog/2017/08/03/search-as-... (disclaimer I wrote it...)
But to my intuition, basic search doesn't feel like a machine learning task. After reading some of the responses to my post however I'm trying to come up with a meaningful reason why I wouldn't consider IDF to be machine learning, given that it is updated as more documents enter the corpus and your system "learns" to re-rank existing result sets based on these new documents.
Because we understand how these algorithms work, we can always reduce them to just this or that. Prediction in many linear classifiers is just dot products. relu neural networks are just lots of clamped dot products. Random projections on simple count data can generate word embeddings.
Whether or not something is merely model-fitting, super-scaling, compression or AI, AI art and machine learning will depend on the field it originated from. It's indisputable that the algorithms are so reducible but I tend to think that we should care more about functional capabilities when compared to an appropriate subset of a known intelligence's abilities than details of implementation.
I guess you can make the argument that even tf-idf as described in the article is a form of unsupervised machine learning because you obtain ("learn") the idf from the data.
If you want to apply machine learning to search then you need clickstream data, embeddings, or learned feature weights.
The difference between machine learning and "simple" feature extraction is mostly just in the choice of metaphors used to describe the computation, not in any fundamental properties.