What texture is used in this photo?

That's a 'halftone pattern'. Halftones are a method of creating color separations for offset printing printing presses. This image was probably scanned from an offset printed piece.

Offset printing presses don't really have the ability to print shading. Halftones use a series of dots of various sizes in a grid to give the illusion of gradation. In the standard CMYK process, the halftone screen for color is generally rotate at a slightly different angle: 0°, 15°, 45°, 75° being common and resulting in the "rosettes" pattern you see.