Thanks, ladies!
Chris, so these days most people (including Angie in her blog post) use "fair isle" to refer to any kind of stranded colorwork (where you use two or more colors of yarn in a single row, and carry the unused one along behind the other stitches). So yes you are right, it refers to the knitting technique.
If you want to get really technical/detailed, "fair isle" specifically refers to traditional stranded colorwork that comes from the Shetland Islands. The key aspects are 1)only 2 colors per row (but different rows can utilize different color combos), 2) small, simple repeated motifs, often worked in succession so they form bands of different patterns 3) usually worked in the round and then cut open (a process called steeking) for openings such as arm holes. The traditional fair isle sweater is a straight up and down rectangular affair with dropped shoulder seams; this shape does maintain the integrity of the stitch patterns best. My sweater does actually follow these rules, for the most part, although I did not do steeking for the arm and neck holes (I split the front and back and knit back and forth). And obviously mine has a lot of non-traditional shaping.
The hat, if we want to get very technical, is actually a style called selbu, which is a traditional colorwork style from Norway.
This is an informative article by the designer of the hat, which explains some of the main stranded colorwork traditions. But I think it's fine to call all stranded colorwork fair isle if you like!