"Longer term, however, we expect that the performance and feature gap between the Web Player and WebGL will become much more narrow, and we expect that browser vendors will make the Web Player obsolete by dropping support for plug-ins, at which point WebGL will become the prime solution for targeting the web with Unity." --
http://blogs.unity3d.com/2014/04/29/on-the-future-of-web-pub..."Today’s browsers are speedier, safer, and more capable than their ancestors. Meanwhile, NPAPI’s 90s-era architecture has become a leading cause of hangs, crashes, security incidents, and code complexity. Because of this, Chrome will be phasing out NPAPI support over the coming year." --http://blog.chromium.org/2013/09/saying-goodbye-to-our-old-f...
Unity's expectation is that WebGL will replace the need for the Web Player at all, so I wouldn't expect to ever see it for Linux. Linux users will be supported via WebGL.