It looks to me more like an Image Trace from Illustrator than a Cutout effect from Photoshop. The result is similar, but you have more control over the paths with an Image Trace and Image Trace produces curved paths whereas a Cutout gives you hard edges and corners.
See this quick Image Trace:
The "textured" look in your example actually looks to me just to be JPG artefacts, but if you want to achieve something similar you can bring the traced image back in to Photoshop (or rasterize and do so directly in Illustrator) and apply a Dry Brush effect:
It's hard to see the details at this size; open the image at full size to better see the effect.