Hi, and welcome!
Sublime itself is designed to be cross platform, and I do intend to release a Linux version. However, I'm not planning on doing it in the near future: In general, I'd rather have less features and more polish, so it's going to be some time before Linux support is the right thing to do next.
Sublime Text itself is a C++ core with Python plugins, however the vast majority of the code is C++ at this point in time. My hope is to see this change and for as much new functionality as possible to be done entirely in Python.
The GUI toolkit is built from scratch for Sublime.
Love the screen shot!