The rising actions, climaxes, and resolutions still applies even for short stories.

If I were to write a dystopian short according to the guide you were given, my rising action would focus on character establishment and teasing the main concept. This would be journal entry one of a child soldier. I conveniently leave out how old the author of the journal is, letting the language and everyday troubles speak for themselves. The reader would guess there is a war, the journal-writer hopes their country wins, war-themed games are fun to play, the writer is patriotic and hates the enemy thanks to the teaching of adults, and there are older schoolmates who have left for war that the journal-writer misses. Something just doesn't feel right though.

The climax is where the reader realizes the full extent of how screwed up everything is. In journal entry two, the reader finds-out the journal-writer isn't an immature 18 year old, he's 10, and the older people he looked up to that are gone are more like 12-13. The war games and slogans are obvious mental preparation for war, but the child can in no way see that. To him, its all about fun games, awesome shows, and plans to impress the girl he secretly likes.

The resolution is where the full horrific society is laid bare. As the child prepares to muster in the third journal entry, the reader can deduce that he is being sent out as fodder to protect more valuable units. That doesn't bother him though because he gets to go do paradise when it is all over. That girl he has a kiddie crush on got the highest honor of being part of the 211th round kamikaze brigade. Lucky her, she gets the best job! It's up to him to set good example for his siblings because he is the first of the three children that each family is required to submit to the military - the quota was upped recently and the age of induction dropped -- implying the war isn't going well at all. He's going to miss his parents and classmates, but they'll all reunite once everyone dies.