I believe generating the HTML is what the term render means in this case.
Render is the final step presented to user. Users do not see HTML, they see text, boxes with background colors, buttons, those are html elements rendered for visual consuption.
The rendering you mention never happened anywhere in the React JS code. Browser did the rendering internally.
Web is much more than the React "ecosystem".
from js class to dom objects => pre render 1 from dom to html => pre render 2 from html to display graphics => final render