Various textured brushes are utilized for creating a three-dimensional appearance without incorporating any 3D tools. The vector shapes are created using Adobe Illustrator, then digitally painted in Photoshop.
This illustrated style is one that I am very familiar with since I've practiced it thoroughly. It generally consists of sharp edged shading and thick or thin bold drawn lines. The export is always a vector friendly format.
It's all about the process of elimination for this vector style. Eliminate the lines and focus on simplifying the overall shapes. The end result will be aesthetically pleasing and translate efficiently to most mediums.