Ok Tom, going to make this simple. The diagram that you posted is indeed heliocentric, and it is indeed not displaying epicycles. However, the diagram that you posted does not accurately explain retrograde motion without the use of epicycles.
if the position of the sun is directly over the earth, and so to are the planets as depicted by the diagram, then the path in the night sky of the planet will show a loop/ a shape where the path is crosses over itself. This is not what we see when we look at retrograde motion. When we look at retrograde motion we see an S shaped doubling back. If the planets are not over the earth with the sun, then their orbit will encompass the circumference of the earth, and no retrograde motion will be observed unless there are epicycles.