And by parental, we mean exasperated, frantic, pleading, angry, and authoritative all in one.
In the beginning, the Narrator's tone is one of authority. "The time has come," he says as if he's the one who gets to decide (4). But as the poem progresses, he starts to get a little more frantic, putting a little more emphasis on those words, such as when he says "But / please go. / Please!" (22-24).
Then the exasperation begins to set in, as the pleading ways that Marvin can leave pile up and get more and more ridiculous. Finally, there's that pitch-perfect parental anger at the end with "I said / GO / and / GO / I meant…" (82-86). Is there anything more parental than that phrase right there? Well, maybe "What did I say?" or "I said look with your eyes, not your hands," but even that's contestable.
Even though the tone is parental, you get the feeling that Marvin feels he's the one in charge. So, there you have it: a pitch-perfect combo of parental tone and child-like understanding.