...unless I'm wholly mistaken, I think they've got their basic terms backwards, thus:
1) Their diagrams are correct: Diagram #1 shows higher trail to be a product of forks with limited curl towards the dropout, so that the vertical drops from close to the start of the curl, producing more trail. #2 shows something closer to a touring fork (such as my Raven), which is a low-trail set-up. All OK so far, then.
2) In the text that follows, the boldface says that "Less trail equates to faster steering," and "More trail equates to slower steering." Surely this should be reversed? That is, the touring-fork bikes have lower trail and slower steering.
3) The same error (as I see it), is replayed throughout the article.
...
Have I got myself in a tangle? Or did the blogista switch his terms around?
I'm sorry to say, John, that the blogger's text is correct, and you're being misled by drawings intended to make a theoretical point i.e. what happens when you change differently raked forks on a bike with the head angle held constant. Follow with me:
Trail is the distance the centre of the front tire contact patch lags behind the steering axis interception of the ground. (This is often stated as the distance at ground level between a vertical line through the axle centre and the steering axis but in fact the contact patch is not necessarily, nor usually, directly under the axle centre. It's a nitpicky point but we're often measuring small fractions here with decidedly non-linear effects, so it is something to be aware of. The axle centre is merely a shortcut. Motorcyclists speak of "mechanical trail" to distinguish this point. There, now you can baffle the Harley-Davidsons...)
This causes a castor effect, as on a shopping trolley but the other way round, in which the bicycle front wheels are set back (technically: "offset") behind the vertical steering axis, so that the force of force of gravity tries to center the wheel in the direction of travel.
How much this self-centring force is, and the force at the handlebars needed to overcome the effect of trail, which is the result of offset, is what gives different bikes different inherent stability and loadbearing and steering characteristics.
A bike with zero trail, i.e. produced steering axis and contact patch centre coinciding exactly, and thus zero self-centring, will be extremely quick-turning but also entirely unpredictable (technically it will have 0% roadholding and require 100% handling, heh-heh), in a word, lethal.
The larger the distance between the produced steering axis at the ground and the contact patch, the stronger the centring force becomes. Another way of looking at it is that the cyclist turning the handlebars is actually lifting the bike, its luggage and his own weight up over the height differential between the contact patch and the produced steering axis intersection with the ground, for which the algorithm will give everyone migraine, except maybe Jim Kukula. It is enough to know that larger trail requires larger disturbing force to drive the bicycle off the straight line, and less to return it to that line, hence a large trail is a requirement for stability.
Consider a bike with a fixed head angle in which you can change only the fork. Offset the hub forward, and you reduce trail. Offset the hub backward and you increase trail. This is all that the illustration which misled you shows.
Let's make another theoretical case, a straight fork but you can vary the head angle on the bike. The slacker the head angle, the larger the trail, with all that follows, the more upright the head tube, the smaller the trail, ditto.
Now we come to the crux of the matter. Nippy, even twitchy bikes, usually have LESS fork rake than stable tourers. But when you add in the slack headset angle of touring bikes to their fork rake, they have MORE trail as the combination of headset angle and fork rake.
If you were to take the drawing with the touring-type fork and angle it to an inclination more appropriate to a touring bike, you will see that it produces a larger trail than the drawing of a road bike type of fork on a road-angled head tube. Then the text will make more sense to you.
***
I regret to report that you haven't discovered a great contrary truth of bicycle dynamics, John. (I'd love to know the fellow who does.) But you've certainly made a good case for my original encomium being too enthusiastic if this blogger can mislead a thoughtful fellow like you.