Merriam-Webster and Unstructured Data Processing

"I was surprised to learn that words with multiple definitions are defined in chronological order of first usage, and not, as I imagined, some kind of “importance” of definitions."

It depends on the type of dictionary. Merriam-Webster Unabridged (and most unabridged and historical dictionaries; you can tell a historical dictionary by the citations/quotations) do it chronologically. Merriam-Webster Collegiate (and most daily use mainstream dictionaries) sort senses (meanings) by likelihood of use frequency, or importance. As you can see, saying "Merriam-Webster" and meaning one dictionary is incorrect, as they produce more than one dictionary. Source: am lexicographer, have worked with Kory Stamper.