I think placing a larger diffuser, inside the softbox, would probably help more. A second option is a type of diffuser I have, which is a piece of gray mesh fabric with four clips, which goes in front of my 24x24 softboxes...no impact on the light color, but it does diffuse them a bit.
I think what we're seeing on the bald fellow's head is just too much specularity...too much sheen...from the relatively small, focused Fresnel lens in the flash sending the beam into a pretty small area, which creates a hot spot on the softbox front. Speedlights tend to have fairly 'focused' light beams at close ranges...and the inside of a softbox is pretty close. Putting the diffuser cap onto the flash might change the light's quality or its look quite a bit, actually.
It might also change somewhat if the flash unit is zoomed to a wider-angle coverage, so the light is "scrambled" more inside the box, before it goes out through the front panel.
Not sure if the softbox has an internal, suspended diffusing panel, or if it is silver- or white-lined; those three things factor into how "hot" (how specular or diffuse) the light is.