Without context, there are two possible interpretations here:
The preceding context provides enough information for the reader to figure out which train is being referred to. Note that the train does not have to be explicitly mentioned before; for an analogous example, see this example dialogue by ruakh from the comments on Astralbee's answer:
A: "What did you have for dinner?"
B: "A sandwich, from the new deli on Main Street."
A: "Oh? Was it good?"
B: "Eh, so-so. The lettuce was a bit wilted."
Here, speaker B can refer elliptically to "the lettuce", even though no lettuce has been mentioned before, since the context gives the listener enough information to understand that what B means is "the lettuce on the sandwich".
"The train" is intended as a reference to the entire train network (of which there presumably is only one in that particular area) or even to a particular mode of transport in the abstract. Typical examples of such usage might be e.g.:
A: "You don't have a car? How do you get to work?"
B: "Usually I take the bus downtown and then walk. It's not that far."
In this case, without more context, it really could be either. But we do have the context available, so we don't have to guess. Let's just see what the whole paragraph says (highlighting mine):
At the 1932 Amateur Athletic Union track-and-field championships, Didrikson was the sole representative of the Employers Casualty Insurance Co of Dallas and, on her own, won the team award by finishing first in six events, setting five world records (although not all of them in Olympic events). She was disgusted to be allowed to compete in only three events at the Olympics that followed. It was at these Games that the 21-year-old announced to a world audience her phenomenal ability and audacious line in patter. 'I am out to beat everybody in sight and that's just what I'm going to do,' she said when she stepped off the train in California.
It's still not 100% unambiguous, but to me the context strongly suggests interpretation #1.
Specifically, the preceding context tells that the event described in the last sentence occurred at a specific time and place, namely at the 1932 Summer Olympics which — even without looking at Wikipedia — we can guess were held in California (in Los Angeles, to be specific). It's also strongly implied that the person being discussed did not live in California at the time, and so had to travel there — presumably by train (this being well before the era of ubiquitous air travel).
Thus, we can tell that "the train" in this case is short for "the train that she took to California". And that's all there really is to it.