I am not sure if the metal pipe that comes from the floor is called a standpipe but water is overflowing from that pipe as the washer discharges,
The rubber pipe from the machine seems to be OK but there seems to be a clog somewhere in that metal pipe.

It is probably not right at the standpipe (you were right!)... that drain line will probably need to be snaked out.. *frown*... Is this something you think you can do yourself?

Apherribo... check the basement for a cleanout associated with this drain pipe... tell me what you see.

If this just started and it's the same old machine then you are starting to plug up. If it's a new install there are several things to incorporate when setting up a washer drain. What is your situation?