yes, this sort of thing is possible today in most every X11-based linux distro (modulo the protections provided by a few things like subgraph or qubes). It also applies when you use ssh with XForwarding to run remote applications (the server can read and inject input into all of your local X windows. It also applies when a program gets exploited: attackers don't need a privilege escalation exploit to get root if you already have a root shell open in another window (or if they can persist long enough for you to open one eventually).

What is new news is that canonical claims (linked under the word "claim" in this post) "snap applications are isolated from the rest of the system. Users can install a snap without having to worry whether it will have an impact on their other apps or their system". This is misleading. So thank you, Matthew, for bringing attention to this!