433 MHz transmitter works only when I touch a specific part
You appear to have not connected the transmit antenna: -

See also this picture: -

Image taken from this page
And, from your video, you clearly don't have a transmit antenna: -

So, when you touch the chip, your body is acting as an antenna.

As you will see, the rf transmitter and receiver are correctly
connected as they work when I touch a specific part on the
transmitter. If anyone could help me understand what is wrong (and how
to fix it), I really will appreciate

You should connect an antenna then they will be correctly connected.