Such a line is created on a sphere if it is a segment of a "great circle". A great circle is created on a sphere when a circle drawn on the surface has it's center located at the center of the sphere. For example, longitude lines around the planet are all great circles, latitude lines on the other hand are not except at the equator. This characteristic is very interesting. It means that if a spherical Sri Yantra is constructed with arcs of great circles (as it should) we really have straight lines on a sphere. So in a way we are preserving the qualities of the plane Sri Yantra and adding curvature in another axis, both coexisting at the same time. The spherical version therefore adds a new dimension but doesn't loose the basic qualities of the plane figure.
When we look at the overall figure from above (figure 3, left figure) the lines appear more and more curved as we move away from the center. This is because our position is perpendicular to the center point only and because we are relatively close to the surface. If we move around we would see that every line is actually straight when we look at it from directly above. Also if we were to back off far enough the Sri Yantra would look identical to a plane Sri Yantra. Also if we choose to take a very small part of a sphere to draw the spherical form we will end up with a plane version. Because a very small area of a sphere is for all practical purpose flat. The very reason why the Earth was believed to be flat by many people for a long time. This shows that the plane version is not different from the spherical version but is a special case of the spherical form.
A spherical Sri Yantra can be projected in 2D to obtain a plane figure with curved lines.