Best bet for arcs and ellipses is use a proper 2D or 3D drawing package such as AutoCAD or Draftsight, then when drawn transfer to PCB via a DXF interface.
I don't see varying width, just arced trace segments with different fixed width, some overlaid. You can route this way with most PCB packages, I presume with Altium, too. DXF import is reasonable if you want draw specific structures with help by construction tools, e.g. planar coils.
I don't see a copper feature that couldn't be drawn with regular trace segments of fixed width. Even if some traces have varying width, there's hardly a necessity to do so.
In other words - just do it in your CAD system using tracks of a suitable width and do not worry about the varying width you see - it was probably all done with a pen 30+ years ago.