Yes, it may well be, I was or am still a bit confused, but "to extract" has the meaning of to pull something out, to get something out or to take something out. But also in the recipes it is misleading that the aqueous phase is extracted, I unfortunately do not know the exact English term and how it is used.
If I draw the comparison to the Al/Hg variant, where we also extract the freebase after the addition of alkali, IPA is also contained in the aqueous layer, but here we dry over MgSO4 in the freezer and use petroleum ether for extraction., which we evaporate later. It is possible that the procedure is different due to the high scaling, because the steps only pay off on a laboratory scale. Perhaps the experts could answer this question for us. But if no drying should take place here, one has to register a loss in the yield by the contained water in any case.