I tried this pistachio nougat recipe once and it came out great. I've tried it two other times and the nougat hasn't set well at all. I'm thinking that this is because the recipe doesnt list a temperature and I probably didn't reach the correct temperature. Is that a good assessment? Additionally, why are most nougat recipes made by adding the syrup to the whipped eggs instead of the whipped eggs to the syrup (like this recipe)? It seems like it would be easier to reduce the mixture to the correct thickness if you added the eggs to the syrup. Thanks
As you suggest, most nougat recipes require the sugar syrup to be brought to specific temperatures (typically "hard ball" or "soft crack" stage, see for example this page for details of the stages of cooking sugar). By that time, any water that you started out with (in your case in the form of rose water) has boiled off. Simply bringing the mixture up to a boil will not be accurate.
For repeatable results, I suggest you use an instant-read thermometer (or a sugar thermometer) to ensure your sugar syrup is at a consistent temperature. If the nougat does not set, increase the temperature next time.
Regarding your second question: Even in your recipe, you add some of the syrup to the egg whites, to raise their temperature before adding them to the syrup. This is called 'tempering' and is common when using eggs in sweet applications with something hot. In the case of nougat, however, you can probably add the egg whites directly to the syrup, as was pointed out in a comment.