The reason people say not to start your story with dialogue is because doing so throws you into the story without giving you any context. The exposition you give has no background to build off of, and the action that tends to follow feels meaningless to a new reader. Here, that lack of exposition is very prevalent.
The problem I have--and that a lot of your readers will have--is that we know nothing about <PERSON> or <PERSON>. There's tension in the scene, but no meaning. You illustrate the scene perfectly, but that illustration conveys little about the characters.
This line is the problem with this scene exemplified:
Seeing his chance, <PERSON> struggled against the ropes that bound his arms and legs, desperate for escape.
Prior to this, we don't know that <PERSON> is tied up. One can easily imagine <PERSON> being cornered by <PERSON> as he advances on him, or frozen still as <PERSON> blocks the exit and points the gun at him. 627
Without warning, the reader has to completely change the scene to account for it, and that change is both disorienting and disrupting.
That being said, I don't believe you need to scrap this work.
One of the reasons that people say that you should never start a story with dialogue is that there's almost always a better way to do so. Most of the time, that better way is to introduce the characters and setting before the dialogue. With this scene, you can introduce the characters beforehand while still keeping the great scene you've wrote, introducing meaning and character development without sacrificing anything.
A short example:
<PERSON> cursed as he struggled against the rope wrapped around his arms and legs. Once more, he desperately tried to reach for the knife in his pocket, fiercely fighting against his rope bindings, but the ropes held strong against his efforts.
[space to expose <PERSON>'s background]
The door in front of him flung open, and a large man's frame appeared silhouetted by the outside night. <PERSON>, intimidating in all his stature, stood in front of him, a large pistol in hand.
"Talk, or I'll shoot"
...
This example gives <PERSON> a lot more background and the setting a lot more detail. It keeps the tension of the scene, while also explaining what exactly is going on. Obviously, there is room for improvements, but this format provides all the information the reader needs while expanding on your current introduction.
All in all, while you can start with a quote, most of the time there is a better way to introduce your story, and I'm sure publishers will appreciate not starting with a quote. 627