I was just got confused with the below line mentioned in the document. However, it seems it is still the same behaviour (i.e --no-psqlrc).
"Before PostgreSQL 9.6, the -c option implied -X (--no-psqlrc); this is no longer the case."
Whether psqlrc is being processed or not is immaterial to the behavior you are seeing because -c will not resolve the variable reference prior to sending the command to the server.
If you have other non-variable definitions in psqlrc that could affect the -c command (or its output - like \pset instructions) those will now be applied before sending the command whereas before they would not be.
(admittedly I'm not reading the source code nor have experimented to draw this conclusion)