Best I can tell from your pic, it had a prolapse vent. What caused it I'm not sure but one thing that jumps out at me is your temp is way to high in the brooder. At 2 weeks the temp in the brooder should be around 80°F. for the warm spot and be at ambient temp at the opposite end of the brooder.
Have you been having chicks with pasty butt? Too high of a brooder temp can cause this problem. California, Gamble's, and Mountain quail tend to have this condition more frequently than Bob's or Coturnix quail. It's been reported that too low a brooder temp can cause pasty butt too but I haven't experienced that happening with my birds.
Gamebird chicks should have at least 24% protein feed, higher protein for chicks that are being raised as 'meat birds'...28 - 30%. A word of caution, higher protein feed can cause digestive problems if fed for long periods of time; ie, mature birds don't need the higher protein, especially 'breeders', it causes fatty accumulation in the reproductive tract of hens, which in turn leads to reproductive issues.
The only other issue I can think of that might be causing the death's is Aspergillosis - 'brooder pneumonia'. There are several strains of the fungus that cause the disease. A necropsy would need to be performed and lab samples to determine the Aspergillosis spp, or genera.
There is no treatment that is effective! Only strict sanitation protocols will help in the control of the disease.
