2-C-0 LINEAR FORCE The ball will respond to non-linear (angular) force exactly the same as to linear forces only if the application produce forces equally linear to the ball but not necessarily linear to anything external to the ball.
Briefly stated, it is necessary to find a way to compress the ball through a particular point along a particular line, and maintain this compression through the same particular point along this same particular line straight line, through the entire arc of the Impact Interval, and with geometrical precision for consistent control. Study 2-K and 2-N.
To maintain compression at a particular point that point, then, must rotate around the same center that the rotating force does. Not just the physical center of the ball nor the gravitational center – just the point of compression. In other words, the original contact points of the Clubface and ball must remain in contact throughout the entire Impact Interval. This is possible only if the motion – or arc – is uniform. Therefore there must be a perfectly centered action – or a compensating manipulation.
The Illustration below, depicts the Hinge mechanism Sustaining the Line of Compression. These are Top Views, looking down on the Ball from the Players perspective. The Blue dashed line depicts the normal to the plane closing of the clubface.
The yellow arrow band depicts the line of compression at Impact, and is the "Straight Line" that HK refers to in section 2-C-O. The Normal Face to Orbit Path holds the Ball against the Clubface through the Impact Interval. The illustration, Blue dashed Clubhead/Clubshaft depicts normal closing of the clubface. Hinging causes the Clubface and Ball to rotate around the Impact Point. As long as the Impact point remains in contact with the Clubface, the Line of Compression will be sustained until the ball fully separates from the Clubface.
The Illustration depicts "Closing" and applies equally well to both Angled and Horizontal Hinging because Both of these Hinges, as well as "No Hinge" closes the Face the same amount. Although no Hinge will close the Clubface normally, it does not follow that the Impact Point remained in contact with the Clubface. So normal closing of the face to the Sweetspot Orbit is not Hinging and only Hinging can sustain the Line of Compression.
Horizontal Hinging rotates the Clubface and Ball around the Impact Point on a Horizontal Plane Only, and thus eliminates Layback inherent with Angled Hinging and "No Hinging". Layback causes a loss of compression on a line perpendicular to the Sweetspot Plane and thus, tilts the spin Axis.
To simplify all of this for D Plane people, it means that Hinging causes the Clubface and Ball to rotate around the Big Red Dot.