That's an interesting perspective. With SVG, the question of what is content and what is style gets blurred. There might be multiple versions of a logo, for example, for different styling situations, each with different geometry. In this case and in others, you might have different geometries for different styling.
Clipping paths are a particularly interesting item.
It is easy to think of clipping paths simultaneously as geometry and styling. Nevertheless, the above distinction sounds pretty good to me, except for compositing. Compositing naturally belongs wherever opacity, clipping and masking go. In section 6.1, the SVG specification provides some of the rationale for what things were defined to be styling properties. Therefore, 'fill' and 'stroke' are styling properties.