Without a proper definition of what you're looking to be "explained", or a reproducible quantitative metric that you're using to to measure a successful "explanation" vs an unsuccessful one, no it isn't falsifiable. If you provide a detailed framework with clear quantitative conditions, then it might be falsifiable, but as of now, it is purely subjective and it is disingenuous to suggest that's an objective test.
For example, why would an explanation of functional programming (which could include any of a huge number of topics), have to explain to you why it exists? Since it is literally an extension of a specific branch of math, there need not be much more of a reason than 'for exploratory purposes', because often that's the only thing that drives many mathematical innovations.
Secondly, it's important to point out the implicit assumption in that argument, that an explanation of a topic is the only possible source for learning and understanding that topic, which is easily proven false by observing the way humans learn to walk. Do babies usually need a complete and thorough explanation of how to walk before they can master it? No, they go through trial and error and learn largely on their own via experience, and even if they could understand language that early, you'll still likely find it very cumbersome to try and explain to somebody how/why to walk in the kind of detail you seen to be asking of fp articles. Therefore, why can't a discipline/activity like programming or mathematics, also require experience learning to fully grasp? Is there a reason why the assumption was made that it can only be learned/understood via thorough explanation?
And while being able to explain something well is a decent rule of thumb to show competence in an area, it's not universal, as demonstrated by the learning to walk example. Similarly, you can't have a fixed minimum requirement for what qualifies as a good explanation to rate against, because understanding changes and evolves with time. For example, a "good" explanation of how the solar system works circa 300BC, would not be a very good explanation now.