Is there any reason to ever use the GDI functions like:

SetPixel();
Rectangle();
FillRect();
RoundRect();
Polygon();
Ellipse();

Please tell in what situations they would be good for game programing or any other application?

Or are they just deprecated in some sence?

They are nice when you don't want to deal with opengl/D3D and the hassle those things bring.

Especially because those are focused on drawing triangles, when you want to touch pixels directly it's a bit of a hassle.