I've been searching but what I've found was always about uploading a video to Tumblr or about adding audio only on Tumblr. None of the results has a solution for my problem. I just want to display a video that's already uploaded on YouTube, not uploading it to Tumblr. How do I embed YouTube video on a Tumblr text post?
I think you misinterpret what the user interface is saying.
There are two options in the video interface.
You want option 1. If you want to add some text you can use the caption.
Another way to do this will be a regular "Add a Text" Post
From there you can use html and YouTube embed option (using the share link at the bottom of a YouTube video) to place it where ever you wish.