In your approach you are only rescaling the final output activation of the base vgg model, while it seems that multiple activation maps are scaled and summed to the vgg loss in the paper:

We define the VGG loss based on the ReLU activation layers of the pre-trained 19 layer VGG network described in Simonyan and Zisserman [49]. With φi,j we indicate the feature map obtained by the j-th convolution (after activation) before the i-th maxpooling layer within the VGG19 network, which we consider given. We then define the VGG loss as the euclidean distance between the feature
representations of a reconstructed image GθG (I_LR) and the
reference image I_HR

You could get all intermediate activation maps using e.g. forward hooks or manipulating the forward of the vgg model.