Clicking a like button on a youtube video is not the only way to determine you actually like a video by YouTube. The amount of time you spend on a video, the number of similar videos you watch, etc can be used by youtube algorithm to determine your interest or the kind of video you like in order to recommend similar videos.
This is abit similar to what happens in real life. If you spend more time with a particular product for example you could begin to see it "everywhere" you go.