In what time period does the story take place?
This a good question. Like many short stories, the time period is not given. And there is little in the work to pinpoint one. What we, therefore, need to do is to piece things together from what evidence is given.
First, the setting is on the eastern edge of the Carpathian Mountains, which borders the Czech Republic and Romania. The two main figures in the story are Ulrich von Gradwitz and Georg Znaeym, and they are noblemen. They also like to hunt. They also have retainers who go out with them. This suggest that the story takes place in a time where these things - hunting for fun, retainers, and personal vendettas in which the local police do not get involved - were typical of wealthy people.
Perhaps the greatest clue comes from the fact that author lived from 1870 - 1916. So, a reasonable guess states that we are dealing with the early 1800s to early 1900s. This fits the author and the setting.