Reference "Hiji Ate", Sam Coombes, Aiki-do, Volume 3, Black Belt Video, 1999.
Also, "Hiji Ate Kokyu Nage", pages 154-155 of Gozo Shioda, Total Aikido: The Master Course, Kodansha, 1996.
In traditional Shotokan, they tell you that step 1 (gedan barai) blocks a kick, and step 2 (oi-zuki) knocks the enemy over on his back. This is an example of restating the obvious ("this is a block; this is a punch") as if that explained the application. We need to rise above that level.
You can use the first two moves of H. Shodan to illustrate the fact that practically any karate move can be a disguised throw. If you spend your life locked in the Shotokan box, you'll never recognize a subtle technique like this one. Aikido students know it as hiji ate kokyu nage, the "elbow-pressure breathing throw."
Begin with your partner holding your wrists. As you stack up for the downblock, reach across with your left hand to grasp his left hand in the jujutsu "pistol grip" (with your middle, ring and little fingers wrapped around the little-finger side of his palm). As you start the "down block," peel his hand off your right wrist and push it out ahead of you as you step. This rolls his arm into an ikkajo arm bar and wrist lock. It also forces him to stagger an awkward step to the west.
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As you begin the second step (the front punch), his arm is stretched across your path. "Punch" through the space below his arm, and use the fold of your elbow to put pressure against his elbow joint as you step through. Maintain your grip on his hand as you rotate your punching wrist and straighten your elbow for full extension on the punch. This rotation puts sudden, painful pressure on his elbow joint. Done with Shotokan power, this will dislocate the elbow and sprawl the uke on his face. Aikido students do it more gracefully, giving the uke an opportunity to do a forward roll and save his arm.
For advanced students: In Total Aikido, sensei Gozo Shioda points out that forearm rotation and elbow-snap are the ingredients that make this throw work. This is exactly what we mean by futi in Shotokan. Wrist-rotation and elbow-snap are the elements that make the front punch work. This is true in both arts because they use the skeleton for biomechanical advantage. What works for one art works for the other.
The lesson is this: If oi-zuki can be a throw, then anything can be a throw.
Ok, that's the "important" lesson, but you are still looking for the "real" interpretation. That's pretty simple.
The opponent on your left steps in with a straight punch (oi-zuki) to your face. The stackup gesture for your downblock sweeps the punch to your right, acting as a soto ude uke. Then your downblock sweeps his arm down and away to your left, opening him up for the stepping punch that follows.
That is an entirely practical interpretation that exactly fits the kata. Run with it!