From someone not at all involved in the field of computer science where this might be applied... where might this be applied in industry? Very compelling stuff, but I don't have a particular use case...
So imagine I wanted to write a "middleware" piece for that milling machine - maybe it has a slight defect where its width measure isn't exactly the same as its depth measure (I expect modern machines automatically recalibrate themselves, but you can imagine weirder problems that this might not solve). Then I could write a program that would rescale models exported from a CAD application to match the weirdness of my particular machine, by reading the file, making the adjustments, and writing a new file.
For a less industrial example that I've actually done, I worked on a fan translation of a videogame. The scripts were, of course, in a weird format that the original makers came up with, with no publicly available libraries. So I wrote a parser that could separate the actual text lines from the timing information and so forth, allowing the translators to translate.
It's used to parse arbitrarily complex transformations to apply to an image in the URL.
As a result I had to write a parser and interpreter. The thing about a lot of these computer science things is that you don't need them until you do. And then when you do it's nice to know about how they work.