Adding noise to gradient
It's generally a good idea to add noise like this when you're using a gradient, to avoid visible banding in the gradient, especially on smartphones. Often smartphone screens claim to be 24-bit colour but the panel itself is actually only 16 or 20 bit.

The chief difference between the example and your attempt to reproduce it is that your noise is in RGB space, while the example only adds luminance noise (i.e. brightness). You could achieve this by using HSV colours and only adding to the V channel, or with RGB colours and adding the same amount to each channel.