HTML was made with documents in mind. Ever since the web's inception HTML has been pushed beyond its original design specs and now people are writing applications in it (actually they have been since CGI). That interfaces continue to evolve and even replicate "native" interfaces shouldn't be a surprise.
As far as the "right" abstraction on the web... this too is evolving and highly dependent on your application. Are you curating a collection of hyperlinked documents? Or are you writing a drawing application?
If your answer is closer to the latter than the former, then the analogy you're looking for is something more like Postscript, where HTML and Javascript serve as a display language for an output device (a browser), driven by an underlying application.
As far as the "right" abstraction on the web... this too is evolving and highly dependent on your application. Are you curating a collection of hyperlinked documents? Or are you writing a drawing application?
If your answer is closer to the latter than the former, then the analogy you're looking for is something more like Postscript, where HTML and Javascript serve as a display language for an output device (a browser), driven by an underlying application.