Earlier quoted context omitted.
After having just taken my first trip to the big island I was actually very surprised how sparse the retail was. Felt very much like rural America.
They're probably using highly restrictive zoning/permitting to keep it out. Local businesses that are charging tourist prices don't want big box stores (who can't get away with a very big local markup) to compete with and local consumer facing businesses hold basically all the influence in that kind of economy.
There is only 185k people living on the "big island". I'm not sure why people would expect something other than a rural America level of services, when it is really just a small city of people effectively in the middle of no where.
Note that smaller cities in rural America service a much larger population than just the city itself. The island does not have a surrounding population that can drive an hour in once a week to make use of a big box stores.
Google maps says there is a Walmart, Kmart, Sears and a number of other well known American brands. It's not like they are being blocked from entering the market.