Well, yes, the office of president was created to be weak relative to the British monarchy. But the substance of executive power (i.e., what actions are authorized) isn't really the issue, but rather whether anyone other than the president has the constitutional authority to do those things.

Take, for instance, the executive power "to grant Reprieves and Pardons for Offences against the United States" (Art. 2, Sec. 2). There is a pardon attorney who advises the president, but it is solely the president who has the executive power to grant the pardon; in that sense the president exercises the pardon power exclusively (or phrased differently "to the absolute exclusion of others").