It should be possible to build a metal detector using just a smartphone.
Metal detectors don't use radio frequencies. This overview shows the frequencies used by various commercially available metal detectors.
All of the frequencies used are within the abilities of the earphone output of a typical smartphone.
You would have to change the operating principle somewhat, but it should be possible.
Typical metal detectors operate by using the search coils in an oscillator. The frequency of the generated signal is compared to the frequency of a second oscillator whose frequency is controlled by the operator.
Twist the knob on the manual oscillator until the unit stops squealing. Both oscillators are now at the same frequency.
If you bring a piece of metal near the search coil, you will change the frequency of that oscillator.
Your smartphone can't operate that way. You don't have an oscillator for the search coil, you have a generated signal driving the search coil.
The phone generates a fixed frequency signal and transmits it through a coil. You have a second coil connected to the microphone input as a detector.
In the phone, you have a program that generates the search tone and "listens" to how loud the received signal is.
In free space, it will have a particular "volume" that it hears from its transmit coil.
If you bring a piece of metal near the coil, the received signal will get louder (or quieter.)
Your software detects the changes in "volume" and changes the display accordingly.
Since you only need one earphone output to drive the coil, you have the second one free to make sounds to indicate the detected metal. If you try, you could probably make it sound like a typical metal detector.
Not to say the youtube video is real. It could still be a fake by someone with more video editing skills than electronics skills.
Now that you've posted the link, I can tell you that it probably works quite well and is no fake.
You video is a test of a detector made by Akyor.
Not a fake, and probably uses a different principle than the ideas I described above.