Amazon promoting its own brands isn't much different from a supermarket offering its own brand items. Amazon promoting its own brands is completely different from a supermarket offering its own brand items. You're confusing a bazaar with a retail store; the two are nothing alike legally or economically.
The supermarket pays for everything on its store shelves (except, rarely, for certain new products on a consignment basis in which case it only sales for units actually sold). Thus, it is irrelevant to the manufacturer whether the supermarket promotes their store-brand product or the name brand product; they've already been paid by their primary customer. Moreover, in essentially all cases, the name brand also made the store brand.
In contrast, Amazon not only sells alongside its third-party sellers, it uses its access to their sales data to come up with its own competing products. Notably, and very importantly: Amazon does not pay for the third-party sellers products available on its website, the third-party sellers have to pay that.
The manufacturers get paid either way (by the retailer, third-party seller, or Amazon if Amazon.com is the seller). But in the case of Amazon, the third-party sellers on Amazon's website get screwed, and that is where the antitrust concern lies.