That guide is just background reading if you get lost, but you should basically be able to just copy-paste that code to your theme and have it work.
You may be able to pass the width/height params as part of the YouTube URL (as per this post), but this customization is currently needed to change the default way Discourse displays YouTube videos.
I do agree Discourse could handle this better by default though so this customization isn’t needed! @Johani would you consider making this the default for video embeds? Would make for more consistent design (e.g. I believe oneboxes, large images, etc. always display full-width…)