Instead of systems programming interfaces in Win32, you use POSIX. You know, files, shared memory, semaphores, threads, processes, pipes, ...

On the graphics side, though: classically, it's been XWindow: a base library called XLib talks the X protocol and does lower level manipulation; widgets implemented on top of that. With XLib you do things like repaint a window in response to expose events, somewhat analogously to a WndProc getting events.

Wayland has its own libraries.

Then you have things like working with framebuffers and SDL and whatnot.