tankie.tube uses peertube, which uses peer to peer technology. It uses the bittorrent protocol but in your browser. When you watch or download a video on peertube, you are both downloading the video from other users and uploading the video to other users. Other people who are watching the same video will know your IP address.
You download the video by watching it, so it's not any easier to track than that. If anything it's harder since now you can watch it without visiting the site. :rollsafe:
Like Speaker said, it's really no different than watching it in the browser.*
Remember to disable P2P if you're not using a VPN.
*If you're using P2P and watching in the browser, you can see how many peers you're connected to. If it says "1 Peer" that means you're by yourself. Only once have I seen the number higher than one.