I looked at the cited paper[0], and I'm not sure the article author has correctly summarized its findings. As I understand it, the paper says "cyclical climate change probably caused this pattern of extinction->re-evolution (van der Hammen cycles)" and it points to overlapping changes in the geologic record (including canids and their teeth) as evidence of that claim.

I can't see anywhere where the article says "changes in canine dental morphology caused the cat gap."

Edited to say: oh derp, I only looked at the first line of the article - there's a discussion of that connection further down in the article, although it says in the summary that the connection is disputed.

[0]: https://link.springer.com/article/10.1007/s00114-002-0392-1

No, they're saying that dogs evolved to fill the niche usually occupied by cats. Rapid change in dog teeth becoming more suited to eat things that cats eat says something about the presence or absence of cats in the same environment.

No. From later in the article:

> During or just prior to this "cat gap," numerous caniform species evolve catlike features indicative of hypercarnivory, such as reduced snouts, somewhat enlarged canines, and fairly extreme reduction of their crushing molars.

They propose that Felids were pushed out of their hypercarnivorous niche by Canids as evidenced by changes in Canid dental morphology from this period.