The issue was triggered due to the sprite texture not being "clean"; the alpha-channel (and other channels) didn't properly reduce to zero where transparency was expected. The result is that the generated "tight" mesh on which the sprite was rendered, contained many near-degenerate triangles. One of the long thin triangles matches the visible artifact. This is clearly visible when turning on wireframe rendering.

The verified solutions include (a) setting the Mesh Type to "Full Rect", or (b) cleaning up the texture itself (in this case, erasing all texture data outside a well-defined circle in some image manipulation tool).