Homogeneous coordinates is still linear algebra in a 4D space instead of the obvious 3 you would naively pick. Kinda like quaternions where adding an extra degree of freedom suddenly works around some expressivity problem you didn't really know you had but clearly it solves (e.g. gimble lock on euler angles). But the term linear algebra covers high dimensional uses like training neural networks, its the thing that gives us the matrix formulation of stuff.