Sestri Levante โ Napoli Centrale, 21 stops. You board at Monterosso and get off at Roma Ostiense โ which is the only stop this train makes in Rome. Verified from Trenitalia's live train tracker, Jul 24.
Because IC 501 keeps going to Naples. Roma Termini is a dead-end terminus โ trains have to reverse out of it. Through-trains heading south (like yours, carrying on to Latina, Formia, Naples) skip Termini and use Rome's belt line, which stops at Roma Ostiense. So Ostiense is the one and only Rome stop on this train.
You were right that "a train to Termini" exists โ but those are different trains: the Frecciabianca and the (sold-out) direct IC 505 we looked at earlier go into Termini because Termini is their final stop. Your IC 501 is the odd one out precisely because it doesn't end in Rome.
Honest side note: Termini is actually a bit closer to your hotel than Ostiense (~2.7 km vs ~7 km). Landing at Ostiense is the small price for getting the direct 5:28 train with your first-class seats together and no changes.
Off the train at Ostiense 10:15 โ the pre-booked minibus meets you in the arrivals hall (Piazzale dei Partigiani side, by the taxi rank) โ ~20 min to the hotel. Full ride details on the flight-day page; seats + train on the options page.