Trenitalia's Ticketless option is only available for single direct trips when booked online. You can book a combined trip comprising more than one train, but then the only option is Self Service, meaning you must pick up the printed ticket from a machine.
A workaround is to book each train segment separately and choose the Ticketless option for each - the total cost is the same.
The Self Service option requires you do perform steps:
1. pay online for the train voyage and get a PNR via email
2. before departure queue at the Self Service machine and get a printed ticket
3. queue at the counter and get a receipt for your ticket
4. get on the train
Step 3 is not required for legally getting on the train, but without a receipt you will not be able to claim expenses from your employer or from any tax authority.
Keep in mind that sometimes: the machines are out of order; the queue at the counter is very long and slow moving.