"Retail giant" would sound better. You are correct.

It's OK. I googled some business news items and found quite a few using the term 'giant retailer'. You're right that 'retail giant' is more common, but there's there's nothing wrong with referring to a company as a 'giant retailer'. You do have to get the stress right, though. 'Giant' is an adjective here, so the stress has to go on the noun 'retailer'. If you stress 'giant', you're talking about a company that sells giants! 'Giant' is also a make of bicycles - so 'Giant Retailer', with a capital 'G' and the stress on 'Giant', would refer to stores which stock these bikes.