Translation:They are going to the train station by share taxi.
the English translation is unnatural. We say "by bus", "by train", "by x", not "by a bus". The only case where we'd say "by a bus" is if you've been hit by one.
I am pretty sure that in English "by [some means of transportation]" is a series of expressions that are only used without any article inside. So I think what they have here is a mistake.
The marshrutkas I've seen in Kyiv were more similar to buses (numbered, fixed routes, etc.) than to cabs. But I can't speak for all of Ukraine, and as a foreigner I may be missing important subtleties.
I think in other lessons I've seen it translated as city bus though. So, if you are right, those are the ones that are wrong.
Kyiv's public transportation system is much better than in some other cities. I do not think it has marshrutkas anymore. I believe people call the smaller city buses marshrutkas just out of habit.