Technically, you should have extended the slope outside of the fence so that the ground at the pool area was more or less level. If you couldn't extend the slope, you should have built a retaining wall in order to level the ground.

You should be showing us a picture of what you want privacy from.

Given the limited amount of space between pool and fence, I think you'll want small tree forms, preferably something not too wide, instead of large shrubs. Shrubs that grew tall enough to screen the houses, will want to spread wide into the pool deck space. There are some tall, skinny ones, but it will take a lot of them. Small trees can occupy much less space at the first vertical 10' of ground space. Small trees can be made out of many large shrubs. (You do not say where you are located.)

The "soil" looks like pure rocks. Will things grow in that?

I'm in north east Arkansas' on a small mountain. There are a lot of pine, maple, and cottonwood trees in the area. As well as ornamental grasses. My biggest concern is how to plant in that small area. Do I need to build a planter box and fill with soil? I can't just dig a hole and plant because the bed would be lower than the pool (and there's a lot of rock). I have been told I can't just fill with soil because it will destroy the fence. Thanks for all your help with this! I really have no clue when it comes to these things.

It really seems that the best strategy for the long run is to raise the fence and extend the slope, as Yard rued didn't happen in the first place. It may not be as difficult as it seems. If the posts are pressure treated, maybe you can just remove the panels and re-attach higher up? Raising the fence will also give you an immediate foot or two of privacy. What is the equivalent cost in time and money to cover the same area with plant material across that distance?

It boils down to raising the fence (and raising the slope or adding a low retaining wall/curb type of structure below it.) Or accepting the grade as it is. True, you can't heap soil up against the fence. While the slope above the fence is not ideal because it creates a difficult area to maintain and a less attractive presentation, it can be hidden with plantings. A hedge about 30" height would solved the problem. If unseen, the grade dipping down would eventually be forgotten about. If you don't get any plant recommendations here, you might try the trees or shrubs forum or the regional forum that covers yours area.

All the rock would be hard to plant in but we don't know what's around or below it so no way to predict if something could grow if you could carve out a planting hole. I see grass, trees and shrubs growing in the neighborhood, so it can't be impossible.

Why do you need 3 ft of deck on the fence side of the pool? Since privacy is important to you, I would make a retaining wall the priority, keeping the deck narrow so that you have more room for planting trees. You could have the contractor form concrete planting boxes as JSL described, or add planter boxes once you have a retaining wall. Then plant some ornamental trees.

Hopefully the contractor is handling all the runoff that could end up in the pool from the sloping yard on the right side.

I'm going to make a couple of assumptions: The fence is in place; it's not moving. There's going to be minimal soil prep to accommodate whatever planting you do between the fence and the poolside decking.

I'd have done a retaining wall out from the decking, and whatever privacy screening, plant or fence, done at the top of the wall. I'm sure the fence has been there for a while and there's budget issues...or some story similar. There always are, and it always is.

IF what you have to work with is a narrow planting space, then you plant things that can fit in that space. I'm going to assume you want evergreen? and fast? and narrow? then for all practical purposes, arbs it is. If you are open to small trees that could branch out to one degree or another, then there are a number of plants suitable...slender silhouette sweetgum, for instance. there are a number of fastigiate trees that would fit a similar profile.