@mfalkvidd First thing one does is to follow instructions exactly and hope things will work out. They don't. You try a different type of connection. Which one? Why one or the other? Which option among the same type? It doesn't work, either. Now, you are thinking, ok this guide is for several controllers, so how do I adapt it for my specific case.
The point being, you can't adapt the instructions on your own. You have to ask someone who's done it before and knows what commands to use in order to make Gateway connect to the specific controller.
For example: using
--my-gateway=ethernet --my-controller-url-address=YOUR-CONTROLLER-ADDRESS
will never connect your Gateway to Domoticz. How can one know that this is the line to be modified?

@mfalkvidd Of course. Skipping test is a bad idea. It is obvious, though that people who resort to asking questions on the forum have tried the test step several times to try and figure things out for themselves. Maybe if the https://www.mysensors.org/build/raspberry wasn't misleading they would even succeed.

@mfalkvidd Removing --my-controller-ip-address did in fact solve the issue.
Thank you for your help.
So, to sum up, these are commands to be used when configuring Gateway for Domoticz ethernet (LAN) connection:

./configure --my-transport=nrf24 --my-gateway=ethernet

make
sudo make install

sudo systemctl enable mysgw.service # << adding to boot
sudo systemctl start mysgw.service # << starting

@mfalkvidd Right. This is the Domoticz's part of the setting

And I configured Gateway like this:
./configure --my-transport=nrf24 --my-gateway=ethernet --my-controller-ip-address=192.168.1.120

make
sudo make install

sudo systemctl enable mysgw.service # << adding to boot
sudo systemctl start mysgw.service # << starting

@NeverDie There are two serial ports available in Domoticz. Right? And you have to specify which one you are using in Gateway configuration. Right?

@mfalkvidd It's a good advice, unfortunately it didn't resolve the problem.

@NeverDie I have no idea.

@mfalkvidd @NeverDie I tried all sorts of combinations. Like for example:
./configure --my-transport=nrf24
./configure --my-gateway=serial
./configure --my-serial-is-pty
./configure --my-serial-pty=/dev/ttyMySensorsGateway

and in Domoticz MySensors Gateway USB with dev/ttyAMA0

then
./configure --my-transport=nrf24
./configure --my-gateway=ethernet
./configure --my-controller-ip-address=192.168.1.120
and in Domoticz MySensors Gateway with LAN

I used other different combinations and this is as close to the connection as I could get

I feel like I'm missing something.

I triedsudo ./bin/mysgw -d and the Gateway seems to be listening

What can I do next?

Decided to switch to Domoticz, ran into problem.
So, Domoticz

and Gateway
https://www.mysensors.org/build/raspberry
got installed.
How does one make them talk to each other? Any help is appreciated.