My truck is a 2003 Chevrolet Silverado 1500 Extended Cab 5.3L Z71 Z82 6.5 ft. bed with 3.73 gearing.
so your truck should be good for 8800 lbs. As for how you can tell what axle ratios are on the chart, there is a key somewhere that has letters like a,b,c,d,e and i think f. I belive d and e are the 3.42 and the 3.73 in that order so 4.10 should be f. Correct me if i am wrong.
edit: if you go at the end of page 2 into the beginning of page three, if you look below the s10/sonoma listings, there is a key.
A: automatic trans
B: manual trans
C: 3.08 axle
D: 3.42 axle
E: 3.73 axle
F: 4.10 axle
also if you go to the chart on the right on page three, the very first listing is your truck with the 3.73. The "e" should be at the end of the towing rating. The left number is for conventional towing and the right number is for 5th wheel towing. So, your 2003 1500 5.3, 6.5 ft. box Z71 tows 8800 lbs. conventional and 7700 lbs. with a 5th wheel and those are with the 3.73 gearing.