You understand it. It's using the word "parse" metaphorically, to mean "validate, then put it in a specially marked data structure". For example, `parse_int :: string -> maybe int` is a parsing function, and it "validates that the string is an integer, then puts it in a specially marked data structure called int". However, the post uses the word "parse" not only for true parsing functions (that convert text into a data structure), but also for conversions from data structure to data structure.

I also find this a confusing use of the word "parse", and it's not explained in the post, and I think "parse, don't validate" is a poor slogan as a result. The traditional slogan is "make illegal states unrepresentable", though that's a bit narrower of a concept.