"I am responding to him."
Translation:Táim ag freagairt dó.
That would be “I am responding him”, which is still incorrect, since it still excludes the necessary preposition.
A transitive verb takes a direct object, e.g. “I see the light”. The direct object is what is being “verbed”, so in this example, “light” is the sentence’s direct object because that’s what’s being seen. An intransitive verb doesn’t take a direct object, e.g. “I gave at the office”. In this example, the thing that was given wasn’t identified; the office itself wasn’t given (which the prepositon “at” makes clear), so “office” isn’t this sentence’s direct object. An example with both a direct object and an indirect object is “I threw the ball to him.” Here, “ball” is the direct object (the thing that was thrown) and “him” is the indirect object (in this case, someone affected by the ball being thrown).
táim á fhreagairt can be a translation of "I am answering him". As Irish uses the same verb for answer and respond, and in English "I am answering him" and "I am responding to him" mean the same thing, you could argue that táim á fhreagairt means the same thing as táim ag freagairt dó, but as you were asked to translate the intransitive "respond" rather than the transitive "answer", you should include the dó.