Confirmed that they are not considered a small business based on amex criteria, they do too much business, they would have loved to participate and accommodate
Im not so sure they are excluded.
You can be pretty big and still an SBS "small business".
They certainly have less than 25 locations.
I'm not going to shop there, but if someone wants to email ShopSmallHelp@aexp.com to find out for sure, please report back.