Details are scarce at the moment, but the announcement does state that there won't be extra royalties involved with deploying to Linux and that they won't be offering Linux support for the editor at this stage. We also have confirmation that this will be landing in a 3.x release, which hopefully means that we'll see an easier migration path for existing CryEngine 3 games than would exist if Linux support were landing in CryEngine 4.
One thing worth noting, is that with the announcement being specifically about updates to the the EaaS EULA , it's unclear at this point in time whether or not full licence holders will be getting access at the same time.
Below is an excerpt from the full news update:
QuoteLet's talk about the pengui... elephant in the room If you read the above paragraph, it might not come as a major surprise to you, but we are proud to announce that we will add an Open GL implementation and support for running your EaaS games on Linux with one of our next updates. For now, Linux support will be limited to the game launcher, and the Sandbox editor will still require Microsoft Windows. And of course, Linux support will be subject to the same developer-friendly terms as on Windows: Your monthly subscription fee will allow you to sell your games for Linux in addition to Windows, with no additional fees or royalties required.
While we can't pin an exact date on this update, we wanted to give you an early heads-up so you can start planning your Linux ports today!
It's nearly been 2 years since Crytek advertised for a Linux developer, and in the meantime, developers of games such as Evolve, StarCitizen, SNOW, Kingdom Come: Deliverance and CryTek themselves with Homefront: The Revolution have shown signs of interest in supporting Linux.
It's going to be exciting to see how this unfolds across the rest of the year!

Game developer, Linux helper person, Launceston coordinator of TasLUG, handsome random steamlug community member, and independent writer/interviewer.

Currently working on Winter's Wake, a first person text adventure thing
I do more stuff than could ever fit into a bio.