This is not a good translation or description of what the cooked chicken looked like. It was probably juicy chicken, or moist tender chicken, which is very delicious. You don't describe food like that as "sweaty or sweating". Instead, the chicken was full of juices and had a wonderful aroma.
Sweat means to perspire when you are exercising, or when you are very hot, and sweat is running down your face and body. That is smelly, dirty, and that's when you take a shower to clean up. Cooked food should not be described in that way, but I guess that got the point across, that it looked "sweaty".