It was two teams working in parallel the one from Virgin and the other from westwood. Both publishers had the "dune license".

The wiki page about dune 2 reveals more insight into the timeline: https://en.wikipedia.org/wiki/Dune_II#Development

Funnily enough the developers of Dune 2 thought Dune 1 was cancelled and were suprised when the Cryo team released early.