The Rockwell HGS doesn't need enhanced or synthetic vision for takeoffs as low as 300' RVR on approved runways. With suitable runway lights, even the HGS isn't required for takeoffs as low as 500' RVR.
Clearly you'd need a takeoff alternate in either case.
You have VERY limited cues with visibility that low, but less is required to fly off of the runway than is needed to land on it, so it is approved and even somewhat routine in places like Salt Lake City and Seattle.
So what IS the takeoff guidance system, or in Rockwell vocabulary, a Head-up Guidance System? It is a HUD very much like in a fighter, with all primary flight instrumentation and guidance visible directly in front of the pilot, so the runway lights and the localizer guidance are superimposed, and the latter is visible even if a dense patch of fog obscures the former.
With enhanced vision, an IR picture from a camera mounted near the HUD is superimposed as well, and depending on the capabilities of the IR, you may never be in weather below Cat I again!
Added: Rockwell HGS promo video
Added: Rockwell Synthetic Vision video
Added: Gulfstream Enhanced Vision video