It does exercise executive power, otherwise it wouldn’t be constitutional. Only congress can make laws. When Congress delegates rulemaking authority to an agency, the agency makes rules pursuant to the executive power to execute the laws.

For example, Congress can ban “unfair competition.” But it can leave it to the executive agency charged with enforcing the law to define rules for exactly what constitutes unfair competition. That’s permissible because deciding exactly what’s unfair reasonably falls within the scope of enforcement discretion.