I don't see a huge emphasis on Euclidean constructions, at least not in this particular curriculum. Euclid is just one book among several math books here. However I do think one issue with studying math from a great books perspective is that the level of prerequisite knowledge it takes to even read a lot of texts considered great would take many years of focused study to develop. I don't see Grothendieck in this list for instance. An intelligent child can read Euclid and follow along perfectly, because there isn't really any prerequisite knowledge needed.