So I get in a weird way,

I could be extremely wrong so take this with a grain of sand but the domain is something that you already know you need for the sentence to make sense.

He overcomplicates with the explanation but to make it easier for everyone my tip is to work it out like a normal problem we were taught then push up the things you need for the sentence to make sense.

For example:

"If the dog barks, only then it will get in trouble"

Take your sufficient and necessary clauses like you were taught then kick up the rest so for example

Bark -> trouble

You kick up dog because you know if their talking about any other animal the sentence isn't valid.

For another example lets use question 4, you know you have to kick up Journalism because you know if they talk about any other form of writing the sentence is invalid. (Fiction =/= Journalism) therefore replacing journalism would render the whole clause invalid.

I think this whole lesson is about moving the information you already know needs to be true in order to better focus on what the sentence doesn't answer.