The "angle of a record's groove", whatever that means, is not the origin of the need for an anti-skating force. That's a misunderstanding.
The anti-skating force compensates for the tension in the arm which pulls the stylus more heavily against the inner groove, due to the position of the arm pivot. This imbalance would still occur if you replaced the record with a straight track. Let me repeat that to be clear: imagine that instead of a record you created a long grooved vinyl 'tape' which was dragged under the stylus. Imagine also that just as with the record, the arm's pivot was displaced sideways (towards the side where the spindle would have been). The anti-skating force will still be required even though you are playing a dead straight, non-circular medium. That's because the arm can only pull towards its pivot, which means it pulls more heavily against the inner groove than the outer. Here's a diagram to make that clearer:
So anti-skating force would still be needed if the record was in fact a straight line. (From the stylus's point of view, it is.)
During playback of a record, the offset (perpendicular distance from groove tangent to arm pivot) doesn't vary very much, so, all else being equal, the anti-skate force shouldn't vary either. Let me be clear what I mean by offset. I am referring to the distance between the arm pivot and the tangential line extending from where the stylus meets the groove, as shown in the diagram.
A sudden loud passage almost certainly increases the drag on the stylus, and anything which increases drag on the stylus will need a corresponding increase in anti-skating force. So correct anti-skating force varies from one second to the next in normal music. It varies with stereo imbalance since a stereo record has differing drag on each side of the groove, it varies with vinyl texture, it varies with temperature and so on. Consequently, anti-skating is a very crude average. You might set it correctly for a mono track 3, but it will be wrong elsewhere on the disc, sometimes by a large divergence. That's why some manufacturers say it doesn't matter. It's never right, and yet somehow the record produces spellbinding music.
I know of no examples of pivot arms where anti-skating is accurately maintained.
Note that he says groove velocity affects it, but then draws the wrong conclusion at the end, unless he thinks higher groove velocity produces less drag.
I don't believe this. It might be so with entirely silent tracks, but as soon as you have musical content you have the likelihood that drag increases with groove velocity. As I've said, you can test this with a conical stylus by observing the movement of the stylus when it is placed on the flats at the beginning and end of a record. Better still, if you have a blank pressing it's very easy to see. When anti-skating is balanced at the track three position, track five will cause a centrifugal movement, and track one will produce a centripetal movement. Don't take my word for it - try it. This shows that an inadequate anti-skating force at track one is an excessive one at track five. Ergo correct anti-skating should reduce as the record is played. The reason is clear: drag is proportional to radius (plus some other function).