I'm looking for a way to do that type of blur with Photoshop.
You can find more examples on Wiz's Instagram account.
It looks like this was an instagram filter and whoever designed the filter seemed to be trying to emulate a cheap polaroid camera with aged film. The tell-tale signs being a poor lens (ie, the blur), blown-out contrast, and a bit of yellowing (as the film has aged).
There's likely dozens of different ways to handle this. Here's one example I did quickly:
From the top-down:
On second read, I realize you were maybe asking specifically about the 'granular' aspect of the blur. I imagine there are also a dozen ways to handle that as well. In this example, I used the Crystalize filter and overlaid a copy on top and adjusted the opacity.
Filter -> Noise -> Median
Then create a second layer that's 50% gray. On the gray layer do Filter -> Noise -> Add Noise. Change this layer's blend mode to Soft Light and lower the opacity.
It's not a blur. There's a Glass Distortion Filter and plenty of JPG compression artefacts. The artefacts probably are not wanted, but they come when high compression is used.
In Photoshop the distortion filter can be found from Filter > Distort > Glass. The displacement texture is a low contrast, nearly 50% grey grain, which can be made from a flat grey fill with Filter > Noise > Add noise. Its used with Glass distortion filter as loaded texture, so save it into a PSD file to be able to load it.
Example of the texture:
The resulted glass distortion:
Here the JPG artefacts are added generously. The image is compressed to about 80% smaller filesize.