2.8 lbs of milled grain will absorb approximately .34 gallons of water, so if the authors mash tun has .16 gallons of deadspace that would explain 2.5 gallons total water going into the mash tun, and 2 gallons of wort coming out.
However, there is still a confusing detail. Your recipe lists the mash thickness as 1.3 quarts per pound. The problem with that is 1.0 gallons (4 quarts) into 2.8 lbs of grain is 1.43 quarts per pound. To get 1.3 quarts per pound as stated then either you need 3.08 lbs of grain and 1 gallon of water, or with 2.8 lbs of grain it requires only .91 gallons of water. You are right to be confused!
I can't answer why the recipe seems to contradict itself, but I will say don't throw away wort. You should collect all the wort until you have completed sparging, and you'll probably collect somewhere between 2 and 2.25 gallons using the volumes in your recipe on a typical system. Technically, since the recipe doesn't use significant figures, e.g.) "2 gallons" could be anything from 1.5 to 2.49 approximated, so thats right in the ballpark. I'm sure you'll end up with a great beer!