Sometimes, it's better to go to the original paper, from which I borrowed the below figure.
Each of the patches in the original image is represented with a single value in the second stage (after convolution). There are $n_1$ feature maps so each patch is represented with $n_1$ values, where $n_1=64$. They call this 64-length representation as a high-dimensional vector, which I believe is not that high (but that's subjective).
Moreover, I don't think the description in the survey is accurate, because the authors of the original paper talks about these high dimensional vectors in the first layer, while the explanation in the survey says the patches are converted into high-dimensional vectors in the second (nonlinear transform) layer:
Patch extraction and representation: this operation extracts
(overlapping) patches from the low resolution image Y and represents
each patch as a high-dimensional vector
Non-linear mapping: this operation nonlinearly
maps each high-dimensional vector onto another
What I'd normally expect from "converting patches to high dimensional vectors" is flattening, but it's not the case in this paper. It follows three convolutional layers, but due to the convolution sizes, the operations performed has other interpretations.