Yeah, that's not very good implementation. PetaPixel usually have good content, but using a GIF to compare these two images? Come on! You can see the compression artifacts very easily.
Choosing a limited palette in order to save bytes, some might say is compression. If said compression hurts the image quality, some might call that "compression artifacts".
The point stands, GIF was a poor choice for the format here.
You could call those lens flares I guess, but commonly known as diffraction spikes when it comes to telescopes. In this case they appear because of the supporting struts in the James Webb telescope.