Sorry for sounding thick (but I'm going to anyway) what is a dog box and straight cut gears and what difference will it make? I understand what the diff does but the rest is above my knowledge level and I'm too lazy to google/wikipedia it.
A normal manual gearbox has syncromesh hubs to match the speed of the gear prior to it being engaged. They still have a dog ring but they're much smaller and finer, when you crunch a gear it's these dogs you are hearing being buzzed against the corresponding part on the gear, its the dog ring that transfers the drive from the shaft to the selected gear.
A dog box does away with the syncro part and replaces it with a much tougher dog ring, as shown in the last two pics I posted. The advantage being there's no syncro to damage and in theory you can change gear a bit quicker, only thing you need to careful of is that it will let you engage any gear at any speed! ie going for 3rd you could pick 1st and it'll go in no questions asked, a syncro box wouldn't, or it would certainly complain if you tried.
Straight cut gears are just that, the teeth are cut straight across, in a standard gearbox they're helical cut which results in quieter meshing but as a result it produces axial thrust which is potentially more friction and power loss. In most gearboxes like this the final drive has the helical cut the opposite way to counter act it. So this kit has to use a straight cut FD too otherwise there would be a big axial load in one direction which would probably knacker the thrust bearings in short time.
Hope that makes some sense.