Well, yes and no. It depends on whether you call the Linux kernel as what makes Linux the OS or not.
For any operating system there are the kernel components and user space components. The GUI in any operating system is going to be user space.
They also suggest it's a "minimalized" Linux microkernel. I kinda agree with this approach, why re-invent the wheel when you can cherry-pick the parts of the existing Linux kernel to make your foundations. The huge caveat in my mind is, the scheduler of modern OS' is what they were complaining about most. I bet the scheduler is one of the things they took from the Linux kernel.
As for the rest of the project. I don't think there's enough meat in this article to say much, and the very limited free version seems a bit too limited to make a good review of how useful it would be.
I'll wait until I'm told I need to port X aspect of my job to DBOS to see if it became a thing or not. :P