"internet platforms that organise and promote large amounts of copyright-protected works uploaded by their users in order to make a profit"
That's actually a lot of limitation. From my understanding: "organise and promote" means it is not simple hosting, and "in order to make a profit" excludes organizations like Wikimedia Commons and "large amounts" most likely excludes smaller websites like fan sites, and "uploaded by their users" exclude search engines.
It is clearly meant to target a form of abuse that is much too common in the "internet as we know it". It is mostly apparent in sites like PornHub. They live by monetizing content they don't have the rights for, and they use their status as a platform as a way to stay legal. I think YouTube admitted that in the early days, they voluntarily turned a blind eye to copyright infringement as a way to grow ahead of their competition.
It is unfair to legitimate companies who do their best to make sure their content really is original or properly licensed.
And if it changes the internet as we know it today, is it that bad? It will push people to self publish instead of relying on "platforms", like the old internet.
As for the potential for abuse, remember that the article isn't finished, it has yet to be completed, ratified, and tried. Public debate is important and we shall not let everything pass, but IMHO, the spirit is good.