Non stop train from Rome to La Spezia

First of all there are no "nonstop" trains, but there are direct trains. What was the date of the train you are looking for? A lot of IC trains are not yet on the schedule. If it shows running June 6, for instance, but not on June 13, that is probably what the issue is.

Edit - Checking my suggestion, on June 13, I see 8 direct trains a day, starting at 6:05 and ending at 19:45. The first and last are the fastest because they go by way of Florence Campo di Marte. The others go along the coast. There is also a night train from Ostiense station at 11 past midnight.

We wanted to get the 6:05 train out of Rome arriving La Spezia 9:11 am. I had thought there was a direct train with no stops but I must be wrong. The Trenitalia has this train for 33.80 euros per ticket 2nd class. We are going olate August 3:05 travel time

The second option was on Italia Rail - they have a 6:57 for $22. US but takes longer 3:47 travel time. They do not offer the 6:05 train on their site. I was going to go ahead and book tickets to La Spezia, then guess we would just get the regional tickets at the station to Monterosso?

We wanted the earlier train so we could have more time in CT but thinking if the later 6:57 train gets us in La Spezia at 10:44 it might make sense. Thoughts?

When bought well in advance non-refundable tickets for the 6.57 are as cheap as EUR 19,90, and for the 6.05 even EUR 16,90.

Trenitalia has this train for 33.80 euros per ticket 2nd class. We are going olate August 3:05 travel time

As Ton pointed out, if you entered 2 passengers, you got the total price for 2 passengers, 16.90 EUR per person = 33.80 EUR.

The 6:05 is fast because it travels on the high speed tracks direct to Florence Campo di Marte, where it does a 2 minute stop-and-go, not wasting time pulling into S.M.N terminal type station, then 2 more quick stops at Pisa Centrale and Massa Centro.

"Direct" and "non-stop" are two very different things. Non-stop is rare, except between two big adjacent cities like Rome to Florence).
"Direct" means you don't have to change trains, you remain in your seat all the way.
The 06:05 from Rome has the following stops (first time shown is arrival, second is departure):

FrecciaBianca 8652
06:05 depart Roma Termini
07:34 07:36 Firenze Campo Di Marte
08:25 08:27 Pisa Centrale
08:48 08:50 Massa Centro
09:12 La Spezia Centrale

There are few direct trains and several more with a change. The direct train has 8 stops between Rome and La Spezia. There is no non-stop train.

We'll be traveling this leg in October. Any feedback from anyone on which route is scenic, coastal route or Rome to Florence?

You have woken a thread from May, and "marketing" will be getting all the emails indicating that a response has been posted.

I suggest that you start your own question as a separate thread so that you get all those notifications and this one can go back to sleep.