The author uses صِفَةٌ in the definition and gives ضَارِبٌ as the example. Ḍārib is an active participle and an example of a governing derived description. Do not infer that every adjective governs a subject and object in every context; the conditions for an active participle’s operation still matter.
In this example, the nominative أبوه and accusative عمرا are explained through the operation of that derived form.