A knowledgeable Writing.SE user once said you could write fifty thousand times the word 'meow' and call it a novel. Such a piece of writing would hardly be considered an account of anything, even less so a 'story'.
If we dial back from the extreme, you could consider some random sentences, like the one that my computer can produce.
The cow was being held captive for a week to make it easier to find a spot in my heart. The singer wrote me that the film would wait. The first of these, the second of those: he has a very different story but it is not the only reason to be skeptical that the world is actually flat.
No dialogue. Definitively no plot. It is a story in the broad sense of an account of people and/or events, but is it an interesting story? Most likely not.
When someone asks about developing a character, the typical answer on Writing.SE is to make them relatable. Give them something to connect to the reader, be it a goal, a struggle, a particular detail or situation. The same goes to just anything in writing: readers will read what they find interesting, and giving them something they can connect to will grab their interest.
Let's consider an even less drastic example, you could consider a text that is just the description of a landscape. A snapshot of a particular moment in time.
Some hills, a flock of sheep grazing on the side of a barn. A family walking by. The youngest pointing at the shadow of a cherry tree. A car dashing on the road. In the sky a hawk is circling over the fields.
This has no dialogue, and no plot. This is however a story. And, in contrast to what my computer writes, you may now guess what is going on, and even get a mental image of the scene. This may even connect with the reader.
You could improve the connection by using a better style, by evoking more profound images or thoughts. By raising questions in the reader that will push them to continue reading in order to find an answer. If I were to edit the landscape description to include these elements, it could become:
Some hills protrude unexpectedly from the plains around Garning. On the soft slopes, a flock of sheep grazes by the side of an abandoned barn. A family is walking by. It is four of them, with faces covered in dust and sweat. Their legs are shaking, and the oldest staggers every few step, like a sick lamb who does not want to be left behind. The youngest is far ahead, almost hidden amidst the sheep, and turns back his head pointing at the shadow looming from under a cherry tree. Isn't it the perfect place for a final rest? He may be already screaming from his cracked lips, but the words are covered by the roaring of a car dashing on the road that cuts the plain. In the sky a thin-looking hawk is circling over the sunburnt fields.
Details. Picture the image before you write it. Imagine the circumstances. Perhaps the family got lost. Perhaps the hills are a magical place outside of time. Maybe the sheep are aliens sent to kidnap humans, and this family is walking right into the trap. You don't need to tell the plot, or even have a dialogue to create a single scene that contains all these elements. The better you can convey these images the more interesting for your readers to read.
You could even have a more abstract theme. No plot, no dialogue, no characters, and (I tried) not even a bucolic description of the countryside.
The distant Moon is large, round like a screaming face, howling in the night, over the woods. Around here the infinite sparkling eyes of the stars, watching over the dark leaves. Not even the sense of loneliness seems to break through the ticking of time. For time is but one of many directions, and loneliness is immobile.
My suggestion to tell a compelling story:
- define a skeleton of the elements of your story
- expand on them with as much detail as you can image
- cut back to the size of a readable text.
And, stay true to the advice of showing and not telling. You don't need a plot, nor dialogue, not even characters for that matters. All you need is a good idea that resonates with the reader, and practice a good writing style.