There are exemptions in the document and this article also talks about it; it would be good to know what tools we can use (p2p chat etc) that are exempt from this. I guess most people will blindly accept and won't care, but at least people can move if they do care (and possibly convince others).
I would think a peer-to-peer system would not be exempt from this legislation, particularly given my understanding that the EU courts do not look favorably on gotcha-style analysis of laws that are limited to definitions of words used being twisted to claim "I'm unregulated". If you are a developer who works on a chat client as part of a decentralized service, I'd expect both you and all of the people running the network to suddenly become service providers subject to this law.
It's impossible for the EU to apply any meaningful enforcement action to a P2P encrypted chat system made by non EU citizen developers residing in a non EU country. Sure, the EU can declare your app is subject to this law, but then what?
Just not being available in app stores would effectively stop its usage.