That’s a good video, all the tricky info is between 10:00 - 11:30, this is explaining the enabling of the serial port and setting the right port and getting control over this port using root privilege (sudo -s).
There are many variation but basically, you need to check the devices using ls /dev/tty* and select an active port. Sometime it might be simpler to connect a usb-serial FTDI converter on the RPI because it is generally mapping as ttyUSB0 and it is pretty easy to see looking at the /dev you can see appear and dieappears as you connect and disconnect the USB converter.
Another simple test you can do is to read on the serial port using screen
sudo screen “port_name” 57600
You should see funny characters appears, thtas because MavLink send binary messages.
To exit GNU screen, type Control-A k.
Once you can confirm you read datat on the port, MavProxy should start on the port assigned.
There is no magic, just simple tools and logic…good luck