...the OS should be quite similar too, assuming watchOS is anything like iOS and macOS, because macOS essentially is the present day incarantion of NextStep due to the NeXT-Apple reverse takeover ;)
...not very relevant for DOOM of course, because that's just plain C for the most part, but interesting little tidbit nonetheless.
Except plenty of stuff has changed since NeXT days.
Objective-C driver kit no longer exists, its C++ replacement is on its way out, being replaced by a userspace version.
The watch uses watchOS UI KIT, is isn't either UI Kit nor Cocoa, so three generations apart from NeXTSTEP UI framework, which is anyway being replaced by SwiftUI.
watchOS uses a customized version of bitcode as deployment format, which is now being transitioned to actual native code in upcoming versions.
Related to Doom, watchOS doesn't do OpenGL, or NIB files from Project Builder.
For a brief moment NeXT was trying to spread Openstep far and wide. What a future everyone could have had, rather than those locked into the Mac ecosystem. Which is most in this country, actually, so same thing I guess.
...not very relevant for DOOM of course, because that's just plain C for the most part, but interesting little tidbit nonetheless.