Someone used screenshots of my YouTube videos in his website

I think you’re making a bigger deal out of this then necessary. As a video creator on YouTube, you’re building a brand, and him adding your video with a link is actually helping you. You both mutually benefit, and sure he might out-rank you temporarily for that specific video (I’m guessing in a Google search and not a YouTube search) but that will most likely change in the future. Wasting your energy on something like this is a waste of your time, especially if you have goals of becoming a well known brand with a ton of subscribers.

You think Gary Vee or Pewdiepie care about who is outranking them for certain topics/videos??? No, they’re too busy making more content.

Unless someone downloads and re-uploads your videos, you shouldn’t worry about it.