This answer is hopefully a work in progress, because this is a good way for me to make iced coffee to take to work in the morning and I don't know how to answer this question beyond experiementation. I don't really understand the molecular/particle-y science stuff behind it, but there is some science happening here lol. Hopefully someone else comes along with a better answer.
Emmymade described such science briefly at the end of her video that the micro-particles that form the instant coffee crystals become suspended in the liquid between the bubbles which grants the foam so much height and stability. She also tried making it with cocoa powder and matcha, since they're extremely fine powders, but those were not successful. I'd be curious to see if you could do something similar with kool-aid or instant tea powder, but I don't have any on hand, so I'm not sure. You can make a similar foam with dried milk powder, but it's not as stiff as the dalgona coffee foam.
As for sugar, I did indeed try a couple of experiments this morning related to the sugar, and sugar (or salt maybe) is required to get the full foam effect.
The basic dalgona foam, made with equal parts (1 teaspoon in my experiment this morning) coffee powder, sugar, and water will whip up to stiff peaks in a matter of minutes even using a hand whisk. I whisk things by hand a lot anyway, so I might have more speed/endurance than some, but it's still impressive. As I said in my comment, adding a little salt does not harm the foam.
I tried whipping up equal parts of instant coffee and water, and while I did get a foamy liquid.... it remained a sloshy liquid with bubbles that popped quickly. I could hear the foam breaking. It did not build up or lighten in color like the normal stuff. Adding sugar into it pretty much immediately stabilized it, causing it to lighten in color and build up serious volume.
I tried making a small batch of 2 teaspoons instant coffee to 1 teaspoon water, and while it was more stable than the equal parts coffee/water, it still never built up the same volume or really lightened in color. I got it to a soft peak-ish stage, but it still moved slowly across the bottom of the bowl, and the bubbles were visible. It was not a smooth marshmallow-y substance. But I did not hear the foam breaking down too much as I held it next to my ear.
I also tried adding a little heavy cream and vanilla to the basic 1:1:1 recipe, and... that failed completely. There was almost nothing left after I whisked it in for a minute. It maybe foamed up as much as the equal coffee/water experiment.
I tried adding a little vanilla to a batch, and while it did not destroy the foam, it did break it down a bit and looked coarser overall.
I tried adding a little cocoa powder to a batch, and like the vanilla, it did not catastrophically destroy the foam, but it did deflate it a little, and got a coarser texture overall.
I did make some with brown sugar which worked perfectly well, it lightened and blew up to stiff peaks like I wanted, but that's as far as I've gotten.
I don't have any artificial sweeteners on hand, but I might try making some with rice syrup or honey this evening just to see what happens.