Discord isn’t the only Draconequus, and they don’t all adhere to the standard four-limbed-snake body type. Some look a lot more down to earth, while others look far stranger. This is Twilight Sparkle, overtaken by the powers of Chaos and thrown headlong into her greatest fears and stresses. In this form, she tends to think at a far more objective, instinctual level. She is vengeful, violent, and extremely powerful. Normally, magic users have a natural mental block that prevents them from overusing their magic, but a Draconequus has no need for a safety measure like that.
And yes, those are her eyeballs in her chestplate.