This rule adds a chord rather than swapping one, which makes it the odd one of the four and also the most immediately useful. Its condition has two parts: the chord is a dominant seventh, and it has a whole bar to itself. Its transformation gives up the front half of that bar to a minor seventh built a fifth above.
Why that particular chord
A dominant seventh with a bar to itself is a bar of waiting. It has already told you where it is going; it just has not gone yet. The minor seventh a fifth above it is the chord that shares the most notes with it while adding one the dominant does not have, so putting it in front does not change where the passage is going — it changes how long it takes to leave, and gives the bass two roots to walk between instead of one to sit on.
These two chords together are the most common two-chord unit in the repertoire, which is why a bar of dominant so often turns into half a bar of each without anybody discussing it first. In a group where nobody has read the same chart, this is the substitution least likely to cause a collision, because everybody expects it.
Where it finds work
The bridge of rhythm changes is the demonstration. Eight bars, four dominants, each with two bars to itself, and the rule fires on all eight halves — turning four chords into eight and the plainest passage in the form into the busiest. That is not an exaggeration of what players do; it is roughly what a pianist does with that bridge as a matter of course.
On the blues it finds seven bars. On the turnarounds it finds none at all, and the page says so plainly: a turnaround is two bars carrying four chords already, so no dominant in it has a bar to itself, and the condition is simply not met. A rule that reported a match there would be a rule that had stopped reading its own condition.
What happens next
Once a bar has been split this way the new dominant is still a dominant, which means the tritone rule can now be run over the result. This site applies one rule at a time on purpose — a chain of substitutions is an arrangement decision, not a derivation — but the tables make the order visible.