I believe the engine bay should look more black rather than a brown/grey colour 😉
That box you are pointing to houses the engine and transmission ECUs. The pipe next to the washer filler in a cold air inlet, and the missing pipe is the outlet. Of the two, better to have the outlet missing.
I believe the part code is 82776-50020. Not sure it goes anywhere, just diverts the hot air to the front of the vehicle.
You can see the engine bay in this brief video - slightly different to yours as it is a LHD vehicle.