I like to think of it this way - maybe someone else has a better explanation, but this is where I operate from:
If I am moving through uke's center at the point of the throw, then it has an irimi element (granted the lead could also have had an irimi element, but I'm concentrating on the throw specifically). If I am moving uke's center around my own at the time of the throw, then I think it has more of a kokyu element involved. Many throws can have an irimi element (kaitenage, for example, with a step through uke's space), but what sets the irimi family apart is that there is no other wrist/arm/elbow/head control involved with the entering movement. It's just nage, uke, and the entering does the throw.
Hope that helps.