Every good story has an introduction to who and what the story is about ("Act 1"), tells the tale ("Act 2"), and most give an 'ever after' ("Act 3"). Shorts are no different. I would distinguish between a viral video which is often just a 'scene' or snippet of action. I've seen some writers post here snippets of action which they want to call a short. While the action and setup may be intriguing, it is ultimately unfulfilling on the screen. Viewers don't like to be frustrated. If the audience is left wondering (what was this about? who are these people? why should I care about them? etc.), it fails.
Story and structure are related but not necessarily the same. Every film needs a story. How it is told or presented is the structure. For example, I could start in the middle, flash back to the beginning, then jump to the end. This is a non-linear structure. You still need to do strong character development by starting in the middle of the story. But that's an entirely different thread. The story, however, has a linear continuity that the director/writer has repackaged.
For a short, yes, the same principles apply. You may only have 1 or 2 pages of script to accomplish your mission. Also, the notion of 'acts' is artificial, so in shorts they often blend. My introduction of the characters may coincide with the story action (combining 1 & 2) or lead to a crisis which is the resolution (combining 2 & 3).
Another piece that is often overlooked is that the script is only a blueprint. A lot of story is told visually. What goes on in the action line can be as important or more so in a short. To write a good short, it is often useful to watch silent movies and kids cartoons. How do they do the set up, tell the story, and resolve it quickly? To be successful, a short has to tell a story. Fields, McKee, and others provide guidance in making the story engaging.
Here is an example of bad story that would make a miserable short.
"A guy wakes up in his bed, stretches and dresses. He walks along the street smiling, picks up a cup and tosses it into a can. He walks and gets to the bus stop. Waits then gets on the bus. Later, we see him get off the bus. He walks back to his home. He turns on the light, makes himself dinner and eats. He brushes his teeth then climbs back into bed. Light goes off."
Is it a story? yes and no. It has an intro, action, and a conclusion. Is it interesting, well, perhaps to someone it is. Really it is just a sequence of events. Adding meaning to the relevance or seeming irrelevance of those actions lies at the heart of storytelling. What happens between getting on and off the bus? What does he dream about? Is this sequence the dream? When you can take the events and give them a different meaning, you start the storytelling sequence. You transform events and draw in the viewer.
Because storytelling and structure overlap, most intro books treat them as identical when they are different. Create your story (intro, action, resolution) then decide on the best structure (presentation) to provoke the viewer's interest. It's true for features and shorts.