Tawaf al-Qudum is the initial arrival circumambulation, which al-Quduri previously identified as Sunnah for the relevant non-Makkah pilgrim. It falls away in the stated direct-to-Arafat case.
Tawaf al-Ziyarah, by contrast, is the essential visitation tawaf of Hajj. Reaching Arafat does not cancel it. The passage must not be interpreted as a blanket exemption from tawaf.