The question uses the word "decriminalized". That implies that such downloading was previously a criminal act. I don't see anything in the Swiss law that says or implies this. (It is not usual for a copyright law to make ordinary infringing conduct criminal.
Article 9(2) of the Berne Copyright Convention provides that:
(2) It shall be a matter for legislation in the countries of the Union to permit the reproduction of such works in certain special cases, provided that such reproduction does not conflict with a normal exploitation of the work and does not unreasonably prejudice the legitimate interests of the author.
Such laws, which vary significantly from country to country, provide exceptions to copyright. For example, fair use in the US, or fair dealing in the UK. Use of a work that falls within an exception to copyright is not an infringement of copyright.
Article 19 of the Swiss Copyright Law provides that:
Published works may be used for private use.
Persons entitled to make copies of a work for private use may also have them made by third parties subject to paragraph 3
This is part of Chapter 5 Exceptions to Copyright. Chapter 5 includes articles 19 through 28. These define various acts which "may be" done under specified conditions, and which are not then infringements of copyright. This means that neither civil suits nor criminal prosecutions may be brought against anyone for doing such acts under the specified conditions.
It should also be noted that article 19 nowhere mentions "downloading". It permits "making use" of protected works, and in particular "making copies". Downloading is one way of making a copy of a work, but the permission granted by article 19 is not limited to that method of making a copy.