(since I poked at this a little while back, might as well add the information here)
There have been 5 published games in the Dune franchise, plus another that never made it to release:
- Dune (Cryo Interactive, published by Virgin Interactive)
- Dune II (Westwood Studios, published by Virgin Interactive)
- Dune 2000 (Westwood Studios, published first by Virgin Interactive, later EA)
- Emperor: Battle for Dune (Westwood Studios, published by EA)
- Frank Herbert's Dune (Cryo Interactive, seemingly self published)
- DUNE Generations (Cryo Interactive, cancelled)
Now, Emperor: Battle for Dune and Frank Herbert's Dune were both published in 2001, so at that point both EA and Cryo both possessed some rights to produce video games under the franchise. Cryo went bankrupt shortly after (at least in part due to poor sales of Frank Herbert's Dune), and had to cancel DUNE Generations. Cryo was mostly absorbed by Dreamcatcher Interactive, but a few years later Microïds seems to have acquired the complete rights to Cryo's intellectual properties.
However, from digging around the internet, it appears that EA's rights lapsed shortly after publishing Emperor: Battle for Dune, and that Cryo didn't hold the rights either at that time - instead SyFy had acquired bundled TV and video game rights when they produced the Dune miniseries, and SyFy contracted Cryo to build the game. SyFy held some portion of those rights till at least 2003, since they produced another miniseries as a sequel which was released that year.
After that, it appears that Paramount optioned the rights to produce a new Dune film in 2007, but they let the option lapse in 2011 after failing to secure the necessary funding.
It seems a fair guess that all rights have since reverted to the Herbert Limited Partnership, which typically appears to prefer licensing the rights as a bundle (TV, film, video games, etc), but I couldn't say for sure.