Cost of Direct TV Stream

They are not cable boxes but streaming devices. If you want another device, then yes. But you can use any supported streaming device like a Fire Stick, Roku, or Apple TV.

How much additional will Stream Choice cost if I have 4 TV’s?

To answer your question more directly - there is no “per TV” charge.  The monthly fee covers as many as TVs in your home as you wish (with a possible limit of 20).  Each TV will need a supported streaming device, which might be something you already have or might be something that you need to buy.  (The list of supported devices is here.)  There is an alternative streaming plan DirecTV offers (called DirecTV via Internet) which provides the ability to buy DirecTV’s own streaming device, which is customized for the service.  But using this device isn’t required, and even if you do, there’s no fee per se - you’d just need to buy the device.