Not really, there's a heap of Western mythos and styles embedded in TOS amongst the many other ingredients of the show.
However, later Trek series (until maybe DS9 in some respects) did not have this element at play as by then the Western genre had vanished from television screens seldom to return.
But since the Western was about the biggest mainstream TV genre there was in the early 60s it's also not surprising that he mooted it as being similar to make execs understand what parts of the format would be.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist