As pointed out here, saying "I like X" in old English would have to be formulated as "X pleases my body" and the word "like" would represent "body" in that sentence. But it's not clear to me how "like" became a verb in modern English.
Just because you found it in a YouTube video doesn't mean it's true. Even if the video was made by a professor. Like became a verb in modern English from the Old English verb lician, which wouldn't have been translated as "pleases my body" but as "is pleasing".
The OED says that the original root word was lich, which can mean body, but also form or appearance. Thus one thing was like another if it had the same appearance. Perhaps the semantic connection to pleasing is through suitable appearance, but that connection is likely lost in the misty beginnings of the language over a millennium ago.