Unpublished research similar to mine

You need to cite the paper only if you use it or depend on it in your research in some way. However, if you have a section on "Similar Research" then you should probably mention it there. You don't forfeit anything if your work was independent. For purposes of your degree, your supervisor will decide if you have made a proper contribution. For purposes of publishing, the editors and reviewers will decide on priority. Just because you don't cite it doesn't mean that it isn't known.

Independent research on a topic goes on constantly in the real world.

The worst case for you is that if you don't cite it and someone thinks you have plagiarized. But the real world situation is as it is. You can't change that.

I think in your literature review where you point to the gap in studies that look outside of North America, you could add something like, "Little research has applied this theory/concept/idea outside of the North American context (for an exception, see Smith, 2016).

And then cite it in your references as Author, A. A. (2016). Title of paper or manuscript. Unpublished manuscript. Date retrieved. URL.

I'll add another aspect to the main issue that's covered in Buffy's answer. It seems that the working paper is not at all identical to your work. As you say, it is "semi-similar" and focuses on a different region. First, this means that your paper remains original. Second and more importantly, your work and that of your colleague seem complementary. You said you already contacted your colleague without response, but in general, this is a great opportunity for collaboration, for example on a comparative paper. Maybe you'll get a response if you suggest a collaborative project that builds on both of your contributions.