Even if we were to accept that an argument about whether Chairs are faculty is somehow relevant to cost-of-living increases, why exactly wouldn’t they count as faculty?
Chairs are elected by faculty members from among themselves for a 3-year term. They can repeat the term once. After that, somebody else is elected. While they perform their Chair duties, they still do both teaching and service and are evaluated according to the same teaching \ research \ service criteria as all of the other faculty members of the department.
It’s a deranged argument to have because if we start down the road of saying that performing administrative duties excludes you from the rank of faculty, we’ll arrive at a conclusion that there are no faculty members at this school at all. Because all of us have some administrative duties. It’s called academic self-government, and it’s something we all are contractually obligated to do.