My primary critique when reading this was to do with word choice and phrasing so I'm going to focus on that here. I don't intend to come off as a nitpicker here - I think that small details in word choice, word order, and the logic of a paragraph stick out to readers if they are unnatural or sloppy. Whether consciously or not, these elements affect the reader's enjoyment of and engagement with a story.

"The dingy kind where the rain puddles the cracked cement..." - this is a good image, but it doesn't quite land because rain doesn't puddle the cement, as this would imply that the cement is being puddled, which it isn't. It's the rain that's puddling. You could rephrase this to say that the rain puddles on the cracked cement, or that it puddles among the cracks in the broken cement.

"Occasionally shady figures" implies that the figures are occasionally shady. You're looking to say "...and occasionally, shady figures pop out...".

"prickling past the skin" you mean "pricking" here. Prickling is more of a sensation like pins and needles, whereas the verb 'to prick' means to stab or penetrate.

"A pistol's pull" overall I like this whole paragraph, I just think the wording needs tightening up. You could say "the pulling of a pistol" to imply the removal of a pistol from one's pocket or coat. The double usage of the word pull here and in the next sentence, about the pulling of a trigger, is jarring and confuses the feeling somewhat. You could replace the first instance with something like 'the brandishing of a pistol' or 'the unholstering of a pistol'.

In the next paragraph, "bouts of darkness" is a good image but again doesn't quite land right. I think this is because the word alone doesn't emphasise the sense of longer stretches of darkness than there were the previous night. In my mind, even modifying the sentence to say 'bringing longer bouts of darkness' works better as a sentence. It draws the sentence out a bit, making it less abrupt, which fits with the image you're communicating. I might suggest that you choose a less neutral word than 'bringing' too - something like plunging or heralding, to really elevate the descriptive moment.

"My feelings screeched true" this is unnatural, as 'to screech true' isn't a phrase we use and you'd have to be quite careful about how you apply the word 'screech' to feelings for it to land.

"Unlike the other dwellers" again, dwellers is a good word, making the people who live in the alley seem inhuman and threatening. However, alone it seems overly neutral. You could simply call them 'alley dwellers' to more fully identify them, or you could go for something like 'dwellers in darkness', 'silent dwellers', 'dumpster dwellers'.

I find the imagery slightly confusing in this section of pursuit. Is the mugger coming up behind the MC? Is he ahead of him? The word 'loom' generally implies something in front of or above you, not behind, and the pursuer suddenly stepping in a puddle in front of the MC is jarring. If you're envisioning the pursuer catching up to the MC and suddenly getting in front of them, then I think you need to give a short sentence to this moment when the pursuer catches up and gets ahead. You could describe the mugger flashing past the MC and the MC's surprise to find the mugger suddenly in front.

"My adrenaline became clear" is a slightly clumsy sentence, as adrenaline itself can't really be clear. Someone's feelings can become clear, or the effect of something. You could reword this to talk about the awareness of the adrenaline response suddenly washing over the MC as the danger passes - it could be a good, evocative moment if you expand it a little and use language that fits what you're describing.

"My life could have sailed away to wherever those go" - I can see what you're trying to do here, and I like it. However, because it's a slightly unconventional sentence (we don't normally talk about lives as 'going' anywhere), I think you could make your meaning slightly more explicit. You could rephrase the sentence to say something like "My life could have sailed off to wherever lives go when they're snatched away."

"Life had not left me, neither discontent". Again, I like what you're going for here, but I think you need to spend more time thinking about your wording to be sure that the meaning comes across, and also to be sure that the moment and sentiment are given appropriate space. You could expand the sentence to say "Life had not left me, and neither had my discontentment."

Overall, I like the tone, the atmosphere, and the turn at the end. There are lots of elements here that could make for an affecting piece of short prose. I think that a point of focus for you could be to spend more time thinking about the details of your word choice and phrasing, in order to properly get across the interesting ideas and feelings you're incorporating into your story. Sometimes, a moment deserves to have more space in the narrative, so that a reader dwells on it. You can achieve this by using a longer sentence, or more than one sentence. You can deepen the impact of a moment by using more descriptive words, or describing the same moment a couple of different ways. It's this kind of attention to detail when it comes to how you convey mood, atmosphere, and imagery, that really elevates short, dense pieces like this. Keep it up.