That's a fk'ing stupid layout man, I wouldn't use that.
With something like a 400W+ lamp, two PC fans (Not even blowing through the shade) are not going to do much cooling - maybe they're meant to help sweep hot air down or mix the air up inside?
Having the filter sucking air in beside the lamp will help, but why's it in a cool tube if it's not connected to the fan? The tubes are expensive and it's only slowing down convection if it's not being used.
That fan should be connected to the tube and venting out through the filter.
Until you see one of the 6" fans in person, you don't realize how much air they move - it's a lot more than a PC can ever get close to. They sound like mini jet engines when they start.
I used to work for a famous online mushroom company and we sold kits for growing. The guy who designed them was an idiot and I actually felt sorry selling some of the things they were that bad. They also featured things like randomly positioned fans that did absolutely nothing.
This is one of those things were I'm watching the video and it's entirely wrong. It's making me wonder if I'm the uber retard, or them. I'm fairly sure it's them.
When you're paying quite a lot for a fan, filter and cool tube, you want as much heat off the bulb and gone as possible, which means it has to be sucking air straight over the bulb - which is why they designed cool tubes to begin with.
If you absolutely have to keep everything inside the box, try;
box---[air going this way]----> open side of cool tube ----->lamp----[duct]---> fan --[duct / direct]----> filter --[duct]---> outside
For the filter, most people put them outside the tent - so they don't have an exhaust port, they blow air out all around their sides. You don't want that if it's inside your grow space, it'll get way too hot in a small enclosure. The plants will wilt and get heat stressed and your risking a fire.
You'll want one that's sealed with an exhaust side to it that you can point out the side of the box - inline. If you can't get one, you could try making one by sticking the exhaust end of the filter in some drain pipe, sealing round the top of the filter so it can blow out down the pipe and then exhausting the end of the pipe out the box.
Or if the filter is too big to easily shroud and exhaust it, ditch the premades and pack a length of PVC coming off the fan with activated carbon, then out the side - potentially very messy if you don't know what you're doing.
The same would also work if you could shroud the filter and connect it to the lamp with the air being sucked through the lamp, the filter, the fan and then out.
You'd have to be seriously low on space for it to be worth it. That box is small enough without all that hanging off the top.
I've tried growing in small spaces and it's a pain in the ass. I'm no kingpin but it's not worth the effort or cost for me.