If anything this makes Linux support easier, because you no longer have to provide support for an entire virtual machine and all APIs such as Flash or Silverlight. The only software required will be the DRM module itself as everything else can be provided by the browser.
A plugin DRM module will also have to do all of the video rendering and displaying. Because if it just hands the unencrypted stream back to the browser then you could change the browser to simply write it to disk.
The relevant DRM mechanisms will come from Apple, Microsoft, Google, and Adobe. Both Apple and Microsoft have no interest in supporting GNU/Linux. You won't get their DRM on GNU/Linux no matter how simple it is. Google seems to ship their DRM now on the GNU/Linux version of Chrome. But I don't know if the license allows using it in other browsers. Which would be hindered by the fact that Google uses their own unspecified PAPPI. Adobe wants to provide a DRM module for Firefox EME mechanism. But we all know from enough bad experience how well Adobe does GNU/Linux support. Flash on GNU/Linux was even worse than on any other system until they simply stopped it. They recently even stopped distributing Acrobat Reader for GNU/Linux. So yeah, great hope there. Even if they compile the module for GNU/Linux because Mozilla asks them to then we can expect the typical Adobe software safety and quality... Remember HTML5 was supposed to rid the world of Flash, Silverlight, and such things. Not force those binary blobs into the spec.
EME means you rely less on Adobe code than you did previously as they are no longer shipping an entire runtime, just the content protection module.
The only browser vendor who wants to implement EME via a plugin is Mozilla. Simply because there can't be a free software Restriction module implementation (and consequently due to the W3C's efforts there defacto can't be a fully free software web implementation). And Mozilla already made a deal with Adobe to provide the Restriction module.
So no, there won't be a market. It will actually close down the market. Content providers will have to support those four DRM solutions if they want to offer their content on all those platforms. They won't have any choice.