The meaning of that Google Maps itinerary is that a TRE train departs at 1:32 PM with the Texas Eagle departing at 2:18 PM. It's a way to show another option in between TRE's hourly headways without taking up another slot on the screen so there's more room to show other options, like the Greyhound buses it lists.
Yes, if one searches for Trenton, NJ to NYC, Google will give you options for both NJ Transit and Amtrak. The algorithm gives you the itineraries it thinks are best according to the filters and preferences you give it.
The ability to display these itineraries is powered by GTFS, or Google Transit Feed Specification, a worldwide standard format for public transit schedule, stop location, fare, operator, and real-time information.
It's very useful for planning trips locally, regionally, or for a cursory search, but I always check with individual operators for the most up-to-date information. It is the responsibility of each operator to provide Google with correct data, and some are better at this than others, especially involving temporary schedule changes, detours, etc.