Edit: basically, it is just coarse salt.
My understanding for the mechanism by which the salt makes the fruit sweeter is by increasing the concentration of sugars in the flesh that's now surrounded by salted water.
Kosher salt is named for the application of drawing water from meat (which is itself part of the kosher preparation of meat) so it's not too surprising that the salt is also well suited for drawing water from fruits like watermelon.
I use table salt on watermelon and it's great too. I can believe that kosher salt would be better, but I doubt most people would consider the difference immense. But palates vary, so, if you've got both salts around might as well use the bigger crystal.
Is that correct? AIUI the primary way that salt makes foods taste sweeter is due to the fact it attenuates our sense of "bitter".
This makes me a bit skeptical that the type of salt matters much. Perhaps it's simply easier to get the dosage right with Kosher salt?
In my experience, yes, salt type doesn't matter too much except for 1) iodine is sometimes quite noticable 2) very minerally sea salts can add flavors
but the amount does (by weight, not volume). Table salt and kosher salt are both very consistent [1] but I use the latter to avoid iodine
[1] but note the brand, iirc morton's is almost 2x as dense as diamond crystal. when in doubt, weigh.
But also it doesn't have additives like table salt (e.g. iodine and anti-caking agents). Iodine at least has a definite flavor.
It's also very consistently made (though not between manufacturers) unlike some sea salts, and relatively inexpensive so it's the go-to kitchen salt (as against finishing salt) for a lot of cooks; you know what you get in a pinch every time.