The key is that it’s named like a variation of another sandwich. If it was a Spicy Italian in an East Coast version, it would be the East Coast Spicy Italian. However it’s the spicy version of the East Coast Italian, so it’s a Spicy East Coast Italian. Of course, they don’t have a non-spicy East Coast Italian, but I’m pretty sure that’s the thinking.

It's an East Coast Italian, but spicy.

I think “Spicy” would be a physical quality.

Like someone else said I would think about “East Coast Italian” as a proper noun for a common sandwich (ie “peanut butter and jelly”) and “spicy” as a modifier on the whole thing (ie spicy peanut butter and Jelly sandwich)

I'm with you on this, it sounds wrong in that order. They are probably trying their best not to infringe someone else's trademark or something.

We've been inundated with "follow steps bellow para and revert" for so long that "the above text" and "instructions following" don't seem to raise an eyebrow -- let alone inspiring concern about the writer having an aneurysm.

Adjective Order is a bridge too far.