Or is Amtrak just one company, and there are other train companies offering different routes? It just seems like such a tiny number of routes (especially compared to Europe train routes)
Anyway, yes, there are no cross country passenger trains in many states, and even for the states that have them they exist as congressional pork, at this point.
It is much faster and cheaper to drive in the US (the train max speeds are slower than the highways), and slightly cheaper and vastly faster to fly.
Only in dense regions, like California and the northeast, are inter-urban trains a meaningful thing in the USA.
Freight trains, on the other hand, are a much bigger deal in the USA than in Europe.