How to add class in plugin only for network site?

How are you invoking ngob_sitelist_slug?

I’m gonna guess that you are doing something like $my_class = new ngob_sitelist_slug;. Doing it this way would require that your class have a constructor. if it doesn’t, you’ll get an error.

You could still call your class methods statically:

$my_thing = ngob_sitelist_slug::my_method();

Though technically you should add the static keyword to your methods in this case.

Also I see that in your case you are using $this, so you really need a constructor.

EDIT:
I now realize you do have a constructor – albeit a deprecated one.