Ultimately it doesn't matter who is the importer of record and who pays the tariff. If Hasbro is the importer of record and paying the tariff, Hasbro could very easily just pass that on to BBTS and EE because they don't have enough a contract that protects them against price changes. If EE and BBTS are the importer of record then they're paying the tariffs directly. Either way they're paying the higher costs and passing them along to their customers (us).
Amazon may have specific language in their contract with Hasbro that doesn't allow for this, or they've chosen to eat the tariffs for now and not pass it on to customers because they value their "price guarantee" long term more than short term profitability. I would assume Target and Wal-Mart probably also have strong buying power with Hasbro that might protect them more than a small company like EE and BBTS.
Either way, somebody has to pay the tariff and decide if they want to pass it on down the line to the customer. It can even become more exacerbated if everyone is trying to maintain a margin %. If people are trying to achieve 30% margins along the way (factory to Hasbro, Hasbro to retailer, retailer to customer) and there is a 10% tariff paid at the beginning, that will result in a larger than 10% price increase as retailers seek to maintain their 30% margins. In my business we call this margin stacking, and it usually results in substantial lost business.
EE and BBTS are probably also working with other distributors for some of their lines (although maybe not Hasbro). Think Japanese anime or some other types of lines where the manufacturer may not sell direct to US companies and work with another layer of distributors. That could add another layer of margin stacking.
Tariffs are generally a terrible idea unless they're protecting a strategic capability - e.g. microchips, steel/aluminum, etc. The US and Europe haven't made plastic toys in our lifetime and never will.