One contention I have with this description (if I understand it at all), is that the projection into the linear space does not preserve the properties of change

One contention I have with this description (if I understand it at all), is that the projection into the linear space does not preserve the properties of changes in a relation graph. I mean I "think" I said pretty much the same in my reply, but one big issue with word2vec is that the relations, which are graphical, can be projected, but not all changes in the graph can be. Therefore, I think it is not correct that these operations are linear in the sense that they can be equivalent to linear operations in the embedding space. But maybe I just don't understand your description.