I wouldn't even try emulating this properly with the standard GPU rasterizer, except as a fallback mode for underpowered systems. It would be fun to try using Image Load/Store and Shader Storage Buffer Objects, though, in OpenGL 4.6. Just bind a framebuffer object with no color buffer and do all your writes using atomic operations to image objects and SSBOs in the fragment shader. The fragment shader interlock extension might be helpful if it's available (note: it's unavailable in Vulkan!) This is similar to how order-independent transparency or voxel rasterization works.
One possibility might be to do two passes: one to build up linked lists of per-fragment data (polygon ID, color, depth, etc.) and a second pass to sort all the linked lists into the proper order and determine a final color. This is the standard order-independent transparency trick.
You could build up tables as well--for instance, you could emulate the "one span per scanline/polygon" behavior by allocating a table of scanlines for each polygon that you fill with the lowest X coordinate for that scanline and discard fragments that don't belong to the triangle contributing the lowest such X coordinate.
I have no idea if this will actually work--if I had to guess I'd put a 50% probability on it not working out at all. The fallback would be a SIMD scanline renderer. The Image Load/Store GPU implementation would be really fun though :)