This is a tad late but in preparation for the soon™ launch of Homeworld 3 I am running through my second favorite PC game franchise again. I ALSO had a problem with the Launch of HW: Deserts of Kharak BUT I left it on “not responding” after clicking START (on Steam) and went for an “I am very frustrated” bowel movement instead of panic-clicking or killing the process in task manager. It took me a while but after I returned the game was on the Start screen. After that, I started it several times without problems (it still takes about half a minute or so in “not responding Nirvana”).
Sure you may have another problem altogether with your gog version but this seems like something I encountered a lot before on other games. They try to run some garbo-junk launcher or whatever, cannot get it to work and after twiddling their silicon thumbs for a while shrug and start the next process in line (which is the fallback(?) solution and in this case the original executable?) I don’t care for MP so I have not tested it out if that is now disabled, however.
Sounds unconvincing? Yeah, I understand…but I have anecdotal evidence (glares at Stellaris and other paradox interactive-published games in general)