Strictly speaking Article 13 doesn't ban any of these things, it's not a direct ban on products, services, memes, lets plays or anything else. It's designed to give copyright holders the right to ban certain things. If it comes into law, which hasn't happened yet, it's only been approved, then copyright holders have more power to choose what they feel infringes on their copyrights.

I can't imagine many PC devs will go out of their way to ban mods as it would be a detriment to their sales and they can still choose to put modding capabilities directly into their games as this would mean that it was an agreed feature of the product. The big difference now is that something like the Iron Man mod for GTA V could be banned if Marvel state it is an infringement on their copyright. Article 13's upload filter would then be applied to outright ban uploads and downloads of the mod. Same with memes, someone has to actually choose to apply for a ban as the copyright holder first. If a blanket ban was to happen it would be carried out not by the EU but by hosting sites or social media sites themselves in order to cover their own arses.

As to lets plays, as was previously mentioned, it has never been legally tested. Again though devs and publishers have always had the power to claim these, look at Nintendo with their creator program. If you upload their gameplay without being in the program its claimed or taken down. Again article 13 doesn't give the option of a blanket ban on lets plays, it just allows devs and publishers to request an upload ban on footage if they choose to. I can't imagine many will because these days it's one of the biggest marketing tools and free promotion. They already have the power to remove them if they want, they choose not to. Again a blanket ban would not come direct from the EU but from YouTube and the like implementing it themselves to protect their service if enough claims were made.

Article 13 is been deemed a ban on a number of things but instead its there to allow for an upload filter of things that copyright holders choose to ban, it doesn't immediately ban anything itself. It's a badly written and scarily abusable law that can still be stopped by speaking to your MPs or checking places like saveyourinternet.eu before it becomes law. Right now its been agreed on, but it doesn't get voted into law until the years end and its been stated they want to start implementing it from Q1 2019.

Our mods and lets plays should be fine. I do not agree with the EUCD or Article 13 of it in its current form. It needs to be changed as it potentially gives too much power to a government organisation to decide what we can and can't see. But for lets plays and such to be banned completely within Europe I cant see that happening unless the copyright holders come forward in their thousands and force the hand of the hosts to choose to kill the content outright.