Is the transfer case manual lever type or pushbutton? If pushbutton, ATF is not the recommeded lubricant. The factory service manual calls for "Automatic Transfer Case Fluid (GM Part No.12378396)" and does not say "or equivalent". The manual case does specify Dexron III.
The manual specifies GM Goodwrench Synthetic Manual Transmission Fluid, with a GM part number, for the manual transmission, but allows for 75W-90 GL-4 gear oil as an equivalent. So, I would not use it in a modern transfer case, more like the old cast iron ones.
If not a pushbutton tcase, I would use "high mileage" ATF, which has seal conditioner. Do not worry that Dexron III is no longer officially listed on the bottle, its a GM legal department thing. Ford and GM stopped licensing old Dexron/Mercon ATF. The oil companies are now forced to use weasel words on the bottle to let you know its the same stuff. "Universal", "Older Vehicle" or Chevron "MD-3" are what to look for.
My front driveshaft turns free in 2H, but is locked (with some gear tooth play) in 4H, just as I expected. If yours is the pushbutton one, the automatic feature may make it difficult to tell when it should turn free or not.