Gary, if you look closely, you can see a fine dot pattern overlaying the image, and that would probably be better described as a texture than the cartoon like reduced colour bit depth.
You can add the fine dots using Filter > Sketch > Half tone. Add a new layer above the graphic, and fill with 50% grey. Apply the Halftone filter to it, and set its blend mode to Overlay. It's the same method as non destructive dodge and burn, or course, but it works very nicely for adding noise, or texture non-destructively. You can edit the texture layer directly, or do a non-destructive edit to your non-destructive texture, by clipping a levels or curves adjustment layer to it.