So basically, the laws in Switzerland won't change
That picture clearly says that ACTA is above any country's laws, though.
It's a little bit more complicated... It's not the same for every country. By example, in France, international laws are above national laws. In Italy, they must be accepted and included in national laws (again, there are some exeptions, but again, they must be ratified by some superior institutions). Switzerland is even more complicated (
) because we're in a direct democracy (which means that we must vote in order to accept the agreement. A good example would be the adhesion to the European Union ; we voted 'no' and that's why the economic crisis had less visible effects on our country. And international treaties have a limit ; you can't actually do much if one of the country doesn't respect the laws. You can still bring them to the International Court of Justice (ICJ), but again, if they don't want to respect the sentence, nobody can force them. The only consequence will be that the relations between the countries will get bad. And the last point is the fact that a country can't apply his laws in another one (the only exeptions are if a treaty is signed and respected by both countries, and major crimes like treason, genocide, murder, etc...)
tl;dr : The laws are not applicable if the country doesn't sign the agreement because it's stipulated in international law that the treaty is valid only for the designated parties, 'just like' a contract