RED streaming interface
You can tap the SDI output port of any RED camera and feed that to a hardware device that reads 1080p video.  Blackmagic make some things that translate SDI -> internal video stream via PCIe card (Decklink), USB (Ultrastudio), and Thunderbolt (Ultrastudio for Thunderbolt).  This would be the easy way to do it.

If you have a RED DRAGON (EPIC or SCARLET) with the latest firmware, there's a RED Tether option.  It requires a special LEMO->RJ45 cable, and it feeds live video out the ethernet port.  See this article for more info.