I'll look at your video, but the aluminum ridged hose is the hot air hose. It is supposed to run from a heat shield on the exhaust manifold to the airbox and supply hot air during warm up, in order to lower emissions, I believe. It is not necessary unless your state has a visual emissions inspection.

It may actually be doing some harm, since there is a thermostat inside your airbox that opens and closes depending on temperature. The common failure mode for that thermostat is to stick wide open, so that your car is seeing over heated air all the time. This can wear out the Air Mass Meter prematurely.

If you don't need that hose for inspections, remove it. You can also remove the entire air box and check the flapper/thermostat for proper function with a hair dryer, but I usually just glue something over the hot air entry port to delete the troublesome feature.