As others have pointed out, there is no magic bullet. This method would work incredibly well for 90% of subjects taught in elementary school. However, for non-English language learning, additional guidance would be needed - the teachers could nudge them towards Duolingo, various online multilingual dictionaries, etc. I do believe that this system could be used as the core of a new teaching paradigm, but it is not solely sufficient for a complete learning experience to the standards that we have come to expect in America.
For developing countries (which, sadly, Mexico bears much resemblance to), this could be an incredible tool. An internet-connected computer and guidance from involved teachers can easily produce students who are ready to help lift their countries out of economic malaise. In this way, I believe the internet can serve as the Great Equalizer many of us hoped it would someday become. If this method used alone is capable of producing students 70% as capable (by some nonexistent perfect metric) as those in first-world nations, that would still be an enormous leap forward for developing nations. I think these guys are really on to something in this regard.
I find it interesting that as our civilizations mature, we find ourselves oscillating back away from the industrialized American education system paradigms and towards a more holistic, broadly-focused educational strategy using qualitative methods rather than quantitative objectives. Students are not a homogeneous population, and historically we have tried to deal with this issue by ignoring it and cramming them all into the same mold, with minor variations. It makes me glad to see that we are starting to consider that we should instead allow for this variance by designing systems with broader definitions and qualitative goals, to allow the students to grow in the directions they are best suited or disposed to.