Both styles will be needed on both empires, though. You can't build an empire with only theoretical science (though that may be the ideal) and you can't stay innovative just with being skilled. Of course, it might strike me as very odd, since the idea of a "military school" is completely alien to my local culture (well, they have those on the other side of the border, but still - here military training to underage people is forbidden, even when the wartime recruitment age is technically 16 for non-combat assignments). The assumption I had is that if the military is picked that young, then perhaps the training on other fields is started early. I personally had a very long "general education" and "do not have a profession" as I'm having a university background, but taking back a generation I do remember that my old folks started working when they turned 16 (with a few years of vocational training before that).
If we recall the old discussion about mill towns, it might be that the vocational training of the Caldari children starts very early with the basics coming amongst play in kindergarten-style schools, continuing with a bit more practical stuff in primary education, which however stays general enough so that if the kids who do well in aptitude tests can be snatched to other schools. From the chronicle referred to in the OP I assume that the usual age for full-blown specialization comes a bit later (14? 15?) but those who do test well can start early. In this case, the character mentions that he was quite strong for a 12-year old, and based on the tasks he's doing, it might be that he tested well in some "P-tests" too. ("P-test" is the term used by the local military for psychological, logical thinking etc. tests.)