Can I just skip the hot sauce when making buffalo sauce?
The Frank's sauce is thickened (the xanthan gum) so your sauce might be runnier. That's easy to fix with a thickener of your choice. I'd probably use arrowroot or cornflour (corn starch to Americans) because I've got them in the cupboard.  Arrowroot gives a clearer sauce but you don't want to boil it or the thickening properies will be reduced. 

The bought sauce is also likely to be cooked for longer, allowing the flavours to mix, while at least one of your links only heats the final sauce briefly.  That's also easy to fix by cooking a little longer.

Looking at the proportions, it seems like a slightly thinned Frank's sauce with extra butter rather than a sauce flavoured with Frank's.  That doesn't affect the conclusion that it's possible to make your own.