(Haiku developer here.) This is a pretty common misconception, but it isn't true; Haiku doesn't have a "POSIX compatibility layer", it's just natively POSIX under the hood. You can find some elaboration on an old forum thread: https://discuss.haiku-os.org/t/is-haiku-a-unix-like-os/8801/...
I think what I meant is that the OS model of what a program is constrains what we think can be done on it. I can't think of anything that couldn't be done in Haiku that can be done on Windows or a Unix.
When I think of non-Unix and non-MVS i'm thinking more on the line of the IBM i, PalmOS, or the Newton OS. All three are quite alien under the hood to anyone who grew up on a Windows/Unix world.
If that is what he meant than iOS and Android are that, their touch interface allows you to do things which can not be done in the Windows/Unix world which is why the Windows/Unix world is bringing in touch.
Does Haiku/BeOS have a lineage, were they built off of some other OS in anyway or just their own thing which took what it liked from what was already around and started from the ground up?
At the time, Be often talked about it being clean, legacy-free, ground-up etc.
The main _inspiration_ was the Amiga, but not really AmigaOS.
BeOS was built in the still-new C++ but AIUI predates a lot of standardisation of C++ which subsequently happened -- as was Psion's EPOC32 and its later rebranding as Symbian.
Haiku which comes from BeOS. I don't recall the linage of BeOS and the wikipedia entry is lacking but it is not Unix, anyone?