I just checked out EoG and that looks like a basic camp-chest style box, although smaller.
Judging from the white china/porcelain plate tucked into the back compartment, I'd guess that the chest measures no more than 20"-24" long and maybe 12" wide, and maybe 12"-13" high with the lid closed. Can't quite tell from the photo (wish it was clearer), but the box looks like it's been covered with leather, a guess backed up by the tight rows of tacking around the bottom. Also, the interior has been wallpapered (which was common for chests and trunks). In fact, it's probably the wallpapering that's holding those dividers in place.
If my guess is accurate, then I'd say the box is constructed with 1/2" or 5/8" stock, and that the dividers in the main box are about 1/4", although the dividers on the left look a bit thinner, maybe 3/16". Some of the dividers in the lift-out tray look a bit thicker, maybe 3/8". However, the lining in the tray doesn't seem to match the wallpaper and it could be felt or some other heavier material that's making those dividers look thicker.
Speaking of that lift-out lid, I'd guess that it's smaller than the inside of the box. That is, you'd typically expect an insert tray to fit snug and be about the same size as the interior dimensions. But look at those two bottles on the left/front, and the two bottles on the right side -- the necks of the bottles appear to be higher than the dividers. If the tray were the same size as the box interior, those bottles would interfere with putting the tray inside, especially since the tray shape appears to match the level of the dividers. I'm thinking that tray is maybe a couple inches narrow on the front and a couple inches shorter on the right to accommodate those four bottles. (If, indeed, the bottles are part of the kit and not just placed there for photo purposes.)
Note that the box corners are pretty rigidly reinforced with those tacked-on corner pieces. I'm guessing the box itself is simple butt-joint construction -- if it was dovetailed, there'd be no need for the reinforcing. (Of course, those corner pieces may be there to hold the leather on, and it could be dovetailed or box joints underneath.) Can't tell what material those corner reinforcements are, by the way; they could be thin tin or more leather.
Without a physical examination of the box, that's about the best I can do. Only so much you can tell from at 4" wide photo. <g>