The site is incomplete, and there are way, way more trains active at a given time. For instance the Tri-Rail and Brightline (high-speed rail) in Florida each have 5-6 trains running simultaneously. Brightline is notable as the US's first credible foray into high-speed rail. Similarly most major cities in the US have either light rail, rapid transit, or both, which is maybe not included in this map. "Passenger rail" might have some highly specific semantic meaning that leaves these out of this map.
Wow, I don't know why I thought there would be... Way, way more trains active at a given time.
I suppose I overestimated passenger rail popularity in this country.. I knew it wasn't relatively huge, but there's several hundred miles in some cases between trains.