Oh my goodness. please don't do what they are showing you to do in this video. I understand that they are trying to show you an economical way to clean dirty car carpet but flooding your car is not a good idea. Some dirty car carpets need to be cleaned aggressively but, please, never use a garden hose to flood the interior of your car.
The person in the video showing how clean car carpets states that the carpet will dry out in about 6 hours if the widows are left open. Automobile carpets are thinner then the carpet in your home but they soak up moisture just like any other soft synthetic material. There is also a pad under the carpet that can hold moisture and extend the dry time.
I am a professional carpet cleaner in the Tampa FL area and I have dealt with flooded cars that need to be extracted and dried out. I can confirm that standing water in auto's foot well will take days, not hours, to dry out once it has been soaked like it is in the video. Be weary of flooding your car. If the carpet is wet for 3 or more days it will begin to grow mold and mildew.
The solution being used in the video is over kill as well and can put even the most robust nylon carpet to the test. I would recommend a scoop of Oxy Clean to a gallon of carbonated water and you will get he same results without soaking the carpet. I have used it in the past and it works great.