Yes this is mostly the correct idea. The connection to the arduino shouldn't be wires (the raw input I don't think comes out to the connectors) but rather a plug like that on the DC adapter that plugs in to the socket on the Arduino that would take the same plug as the DC adapter has. Connecting 12V to one of the 5V connections will blow up the Arduino. From the Amazon documentation on the screen I couldn't figure out what its power connection is. They seemed to say it was an RCA jack, but that is a very odd (and I think dangerous) choice it mentioned a "power cable" but doesn't have any details about it. That may come out to wires that could be soldered to the DC LUG in the drawing above. Good to hear the circuit is working, does that include the video connection to the Mac? The listed screen seemed to only have a VGA connector not hdmi and I'm not sure if the Mac supports VGA (it may well, I know little about Macs but something to check before buying a screen if you haven't yet 
).
Peter