I use Windows and I don't think I have an icon corresponding to the 'eyeball' you mention.
I can do a right-click and choose Open, or 'Open With' followed by FoxIt from the context menu - this does work. Less convenient than a double-click, though.
Since I initiated this thread I have seen what looks to me like the same PDF interface in other software products and on the web. So I think that it must be a software widget.
However, it seems that very little thought has been given to interfacing it conveniently with Evernote and there are bugs - for example, regarding pasting a num