How long and how wide should the runway be to take off or land a Gulfstream 650 on private ranch property?
75-foot wide runway, and since you'll need to takeoff after landing, the takeoff distance at maximum takeoff weight at sea level is 5,858 feet.
This one is based upon aircraft loadout, field elevation, surface winds and ambient atmospherics. You will have to consult the airplane flight manual and performance tables specifically approved by Gulfstream for use in the particular G650 in question for required runway length. Typical takeoff lengths are therefore going to vary between about 3000 - 8000 feet depending on the variables listed above with a quoted metric at 5858 feet at MSL, calm winds at STP and MTOW.
Often times, the distance to clear a 50 ft obstacle at a particular airfield is more useful to the flight crew than the mere runway length needed to take off; these figures are also published in the performance tables for the jet.
As to runway width, I'm not aware of a specific number for this; at a guess at least 3x the wheel track of the main gear and at least, say, 100ft of clearance for obstacles from centerline. That's still a pretty tight squeeze and unrealistic for normal operations. Given the kinds of airports this jet will likely be operating from, this really isn't concern.