As for your criticism. Spaced repetition is well backed by experiments and centuries of observation and fits with our growing understanding of memory - see Long term potentiation and PKMZeta.
Contextual interference is more tricky as it is not fully understood but it is also long studied. Unlike cargo cult, various hypotheses are being offered, tested and refined. For example, the short-term long term memory observation is based on the observation that in tests of recall, stroke patients with impaired short term memory (regardless of method) and those using the varied examples method performed better after 24h+ than those using blocked practice with functional working memory. The hypothesis being that the constructs active in long term recall are more exercised using the varied examples method, leading to better long term performance. Another hypothesis is that increasing the complexity by interleaving examples increases the challenge level and hence engagement and motivational/reward circuits parts of the brain important for learning. In addition, interleaving examples forces a more general model to be learned, encouraging generalization instead of just short term memorization.
The comparison to machine learning (they use ANNs) is: when the examples do not reflect the distribution from which they are coming from, then the learned model is less general. And in particular, when a new set of examples with different properties is trained on it interferes negatively with already learned material. In the paper they give examples of similar occurrences in rats and humans.
Finally, it is important to note that randomly interleaving examples is not useful when trying to figure something out - where short term memory is key. The observation is that contextual interference disappears for complex tasks, this is because the information requires more complex processing and integration in working memory. The ability to hold more information and more complex models in working memory correlates strongly with the ability to understand things. Interfering with this process leads to poor performance short and long term. As the material is familiarized, compressed and basic models are composed, difficulty reduces. It is here that interleaving becomes important.
The practical implications are when practicing drill exercises, rather than blocking the material according to similarity, interleave the material so a less biased model is formed and the material is more challenging to keep focus. When designing exercises break them up into the core simple, defining examples and interleave these while gradually increasing the difficulty by composing more difficult models from the simpler material and continuing to interleaving these with the simpler basis examples set.
I could be wrong, but the article only mentions research on recall. The conclusions reported by the article match research results on recall. The article features one researcher, who happens to study recall. Now, if you think it's common sense that research on recall says little or nothing about hitting tennis balls or dancing the Viennese waltz, then how are you supposed to read the article? Science writing elides a lot for the sake of brevity and breeziness, but I have a hard time trusting that the author knew about research justifying the same conclusions in the case of tennis and dancing and decided that instead of mentioning how broadly the findings had been confirmed, he would lead his readers to believe that it's all based on one narrow path of research. (Also, I don't think it's a very good defense of science writing to say that an author didn't make a mistake in reasoning, he only encouraged his readers to do so.)
The argument for the latter being if you focus on one thing your brain will rely more on short term memory in working things out. If you vary randomly within the domain, constant switching of context forces more reliance on long term memory structures. So you learn slower per session but show better generalization and retention of material in the long term. Its good if you are just learning but not useful if you are trying to figure something out.
The mechanisms are little understood but what's really cool is that a similar effect is seen in machine learning. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117...
http://en.wikipedia.org/wiki/Varied_practice
http://jn.physiology.org/content/106/5/2632
http://www.cogsci.northwestern.edu/cogsci2004/ma/ma239.pdf