As a Linux user, I'm kind of jealous of
1) Easymotion navigation in any GUI
2) seemingly vim emulation in arbitrary input fields?
Does something like this exist on Linux?
Tiling window managers will generally give you re-bindable keys for any and all window navigation. In fact, for the emacs folk, there's already stumpwm, in which your window manager is configured and controlled from a running emacs instance.
Arbitrary text field input, not so much. Sounds like a project :)
I do use a tiling WM (i3). I was specifically referring to the easymotion[0]-like navigation shown in the video.
What annoys me most about windows is, that you have to resort to using the mouse for many things, and selecting things using something like easymotion seems powerful.