Well, I'd also suggest you to not take this project over. But not because of any legal issues - I totally don't object against anyone taking anything, parts of code or the whole codebase, out of this project to continue the addon or create a new one or whatever. The "all rights reserved" license was probably a bit misleading, so I changed it to "public domain" now.
So legal problems wouldn't be the reason, but technical ones. Most of the ATSW code is just ugly as hell, and it is full of funny chances for race conditions and performance bottlenecks. One of the reasons why I didn't continue development of this addon (besides the simple reason of me not having played WoW anymore for years now) was that it has grown to be unmaintainable over the first years of active development, probably mostly because of lack of an emphasis on writing maintainable and well-structured code on my side. I really wouldn't want to inherit such a wreck, so I can't suggest anyone else to do so. I'm not much into the Skillet codebase, but the last time I've glanced at it (quite some years ago, when it was just released) it seemed to be much better from a maintainability point of view, so it might be a good idea to invest your effort there.
But if there's anything you find useful in the ATSW codebase, feel free to take whatever you'd like! I certainly won't do much with it anymore - I have basically just updated the TOC versions over the last years while the main functionality was at least mostly working without requiring any changes, so people could still use the addon. But of course it was just a matter of time for some API changes to seriously break important functionality - I guess this time has come now, so I'm going to finally abandon this old project once and for all.