Why do the administrators not include spells in the spells and rituals such as non verbal ones like when hope switched her shoes with someone in the last episode or things like spells that only require hand movements or snaps?
Non-verbals are not typically listed. There are occasions where some "spells" come back around that are non verbal but have had a spell said either previously or after the fact. Sometimes given the differences, I don't or can't lump them all together under one instance.
Non verbal or a magical action doesn't constitute being on the page.