Yeah the "redirect somewhere else" attack definitely doesn't necessarily require any particular control of the site. Usually it's noticing that you can trick some text into being run as Javascript, instead of interpreted as text... And then you just stick in a cheeky little <notarealscript>window.location = "https://www.badsite.horse"</notarealscript> into that spot.

Then every time that comment, username, (in this case apparently) custom emoji, etc. gets loaded, whoops, the code runs and off you go!

So no control of the site is required at all.