Is a 100 hour inspection required for an aircraft to be used in a checkride?
The rule is that the pilot may not be "for hire".

He is for hire, but as a DFE, not the PIC (the one flying the plane), so he is not breaking the rule.

You are the one flying the plane (the PIC), but you aren't getting paid (in fact, you are paying someone else), so you aren't "for hire" either.