1. The prevalent tone in this section is irony. (Does the narrator really think of tourists with guns as "sportsmen"? Does he think of bagging the only tiger - a little one - as a "distinction"?)
2. Notice that the authors uses "shoot" in two different ways:
a) "shoot anything else": shoot + direct object
b) "shooting at jackals": shoot + prepositional phrase
The first usage means "to hunt with a gun". The second means "to aim and shoot in the direction of".
Notice how the "sportsmen" (remember the irony) are not interested in deer, peacocks or boars. They want to shoot fierce beasts, like tigers. Jackals are predators, but they're not dangerous. "Shooting at jackals" is a sign of bored frustration. We don't know if anyone killed a jackal, but I doubt anyone took home the fur as a trophy.
Summary: They wanted to shoot tigers, but didn't find any. Out of boredom they shot at jackels, but they probably didn't care if they hit them.