Here's a guide to styling such text:
https://www.w3.org/International/articles/vertical-text/Chinese/Korean/Japanese/Vietnamese originally, but computers have made horizontal writing more common on the internet. Modern Vietnamese is also written in a variation of the Latin script, of course.
Mongolian still uses the vertical Mongolian script, though Cyrillic script m has also been introduced in Mongolia during Soviet times and seems to be common inside Mongolia. However, the Mongolian government seems to be moving back to using the original Mongolian script. Furthermore, the Mongolian people inside China never took up the Cyrillic writing system.
Websites can and do use the vertical script: https://president.mn/mng/ http://khumuunbichig.montsame.mn/index.php?home&readnews=572
Google uses the Mongolian Cyrillic alphabet (https://www.google.com/?hl=mn) so even companies that seem to have a page in every single language don't seem to bother with supporting the original script. This is probably because the Mongolian speakers inside China can't make much use of Google anyway.
Funnily enough, Mongolian is one of the few known scripts not only written vertically but also left to right, unlike other Asian vertical scripts (which go right to left).