what exactly do you mean by 'global parse'? it's very usual, i think, when operating on data stored in files, to parse them into in-memory structures before operating on them? but it feels like you are talking about something specific to vector rendering
slug builds acceleration structures ahead of time. the structures are overfit to the algorithm in a way that ttf should be but which is economical for video games. that doesn't seem like an interesting concern and nothing about it is specific to the gpu
I'm referring to needing to traverse all path segments to determine the winding order for an individual pixel. You can't solve this problem locally, you need global knowledge. The easiest way to do this is to build an acceleration structure to contain the global knowledge (what Slug does), but you can also propagate the global knowledge across (Hoppe ravg does this).