Strictly for streaming purposes, no. In fact, the base line 2.3 GHz unit would work with 4GB of RAM. More RAM makes everything work quicker, granted, but it isn't entirely necessary particularly for video streaming. You do not need the dedicated video card to run full 1080p video.
MacBook Pro (15-inch, Mid 2012) 2.3 GHz Core i7, 8GB, 256GB SSD + 500GB HDD + 1TB FW800 OWC Mercury Elite Pro mini
iPhone 6 4.7" 64GB iPod nano 8GB Sound System Audio Engine A2 Display UltraSharp U2412M 24"