Is there any possibility that Unreal Tournament 1999 GOTY could be brought to Mac using Wineskin (like the Fallout games)?

Good question. I thought there was already Mac and Linux versions of UTGOTY. I do know that UTGOTY will run on Linux via Wine, so Mac should be a go too.
Hell, I recently got a laptop with Linux (Ubuntu) on it. I've been buying more games off of Humble Store than GOG simply due to GOG's lack of Linux support.

I would assume the official version of UTGOTY for MacOS is the PowerPC version so that wouldn't really be an option, wine would probably work. For the Linux version the official version works with a little bit of effort except the linux version of the renderer has no framecap so it runs at about 3000 fps and is unplayable. But if the framerate is limited it would probably be fine or someone compiles a newer renderer on linux. (apparently this involves a lot of work and pain so no one has succeeded)