Regardless of the name, descriptive set theory does not seem to have all that much to do with "set theory" in a foundational sense; it can be recast in terms of types and spaces with comparative ease, and this can be quite advantageous. The article is a bit confusing in many ways; among other things, it seems quite obviously wrong to suggest that recasting a concept that seems to be conventionally related to mathematical "infinities" in more tangible computational terms is something deeply original to this particular work; if anything, it happens literally all the time when trying to understand existing math in type-theoretic or constructive terms.