The wording "or, for commercial operations as commander", implies they are also referring to private flying.
The trick with EU legislation is to read
all parts of the Regulation - in this case, the requirement is "in accordance with 8.e. of Annex IV" and paragraph 8 is titled
"Additional requirements for operation for commercial purposes and operation of complex motor-powered aircraft" Thus paragraph 8.e. and, therefore, the requirement for the operator to designate the pilot-in-command, does not apply to non-commercial operations in other than complex motor-powered aircraft.