I did not see the blue cheese slice on top mentioned in the recipe. Am I missing something?

I see a goat cheese that looks like Humboldt Fog, a goat milk cheese that has a blue vein through the middle. A blue cheese would work here too.

If you like the idea of bleu cheese and persimmon on bruschetta, do a web search.
There are ones with bleu cheese, Brie, and more.

Sometimes the site operators take artistic liberties when presenting a recipe. It looks like the photographer and food stylist were at it again during this photoshoot.

Only the second of the four photographs is close to what is described by the recipe author. As you note, the first one has some sort of veined cheese on top of the persimmon. The third and fourth photos look like botched uploads.

None of the photos show sprigs of rosemary or mint. Peculiar and unexplained but not the first time this has happened on this website.

Curiously, an Internet Wayback Machine snapshot (dated February 12, 2013) shows the second photo attributed to a different photographer and two other incongruous photos.

https://web.archive.org/web/20130212110740/https://food52.com/recipes/20501-persimmon-bruschetta

Anyhow, if you want to make a dish faithful to the author's original vision, follow the written recipe instructions. Of course you are free to improvise as you see fit though.

Best of luck.