How did the horned lizard evolve?
The behavior can be explained evolutionarily just like any other trait. It came about either through adaptation, neutral evolution, or as a by-product of another adaptation. 

An intermediate step, like the one you suggested, is not required. But if it did occur, there's no reason to believe that such a trait would cause extinction. Bloody eyes, whether they squirt or not, could be beneficial in some species. We know that blood-squirting eyes appears to be a defensive trait. Take away the ability to squirt and the blood could provide defense in some other unexpected way, or it may have had nothing to do with defense at all. Maybe the blood was just a lubricant before, or maybe the blood somehow enhanced vision during a stressful event. Or maybe it was just there and didn't do anything; nothing good, but nothing bad. 

There's nothing special about this lizard. It does have a unique trait, but there's something novel in every species.