Short answer is yes, that 800 lbs is for your passengers and cargo in the truck.
The towing capacity is a number that is derived by subtracting the weight of the truck (Gross Vehicle Weight) from the maximum weight of the truck plus the trailer (Gross Combined Weight Rating). The GVW in the towing capacity assumes the driver is 150 pounds, and there are no passengers or cargo. So if you have 800 pounds to play with, that will be the weight of your passengers, cargo, your driver's weight above 150 lbs, and anything you add to the trailer.
When towing, you have to stay under the GCWR of course, but you also have to look at GVWR (the R stands for rating) which is the maximum weight of the truck. This is the dry weight of the truck plus your driver, passengers, cargo, and don't forget... tongue weight. Also, with lots of cargo plus tongue weight, you could go over the rear axle rating before hitting the GVWR.
All of these calculations (with examples) are in the owner's manual. Since your trailer is so heavy, I think you're getting close to the maximum. So I 1up 1Tech's suggestion. Your ST will probably be fine to tow it home when you buy it, but you don't have enough towing capacity to haul it loaded down for a trip. You're in the same boat as I am with my boat. The ST will pull it around locally, say to the shop. But I use my wife's Armada to haul it long distance or on a trip when we're loaded.