Even if you took your own videos, thinspread, you did not own them, unless you own the music rights, have the agreement of the skater, and location that ran the event.
I have plenty of experience with youtube, having had all my videos deleted, including ones of my grandchildren, because I posted a video of the 10th place couple at 2003 worlds in ice dance, who happened to be skating to a John Lennon medley.
My grandson got an initial warning (at age 10) for posting a video of himself, playing the guitar and singing John Lennon's Christmas song.
Yoko is Fierce.
There are very few skating videos on youtube that are strictly legal. Some local competitions allow filming, providing you are not compensated for the video. If you accept Google ads on your video, you would technically be in violation of that requirement. Even if the location did not declare such a requirement, if any of the music cuts the skater skates to are not public domain, your video is at risk from the owner.
If your videos disappeared, and you did not shoot those videos yourself, and you are not the skater yourself, those videos are pirate videos.
What is true about youtube is that once they remove your videos, despite giving you a link to protest with, Youtube never even gives you the courtesy of reading your emails. You will have to hire a lawyer, I guess.
What I protested was that not only they deleted all my videos, they also deleted my google mail id, and my website for a totally non skating or video related activity. They never gave me even the favor of an acknowledgment that they had done so, despite the fact that they had merged my Google & Youtube ids all on their own hook.
I no longer upload videos to youtube, because they are all at risk; it isn't worth the efforrt.
I recommend the same to you.
It is not some bone headed conspiracy against Yu Na Kim & her fans
It is part of the consequences of the Napster court decision on free music distribution, and the push in the UK to protect soccer matches from being uploaded. Skating vids are just collateral damage in an effort to protect copyright on line.
This is a very complicated issue that remains unresolved in the courts. Copyright owners are betting that YouTube posters don't have the money to sue to establish and enforce their rights. YouTube and other online providers are acting in a way that protects their rights, regardless of whether actual copyright infringement is involved. Here is an article that discusses a lawsuit that was filed (and is still pending) following a take-down of a YouTube video involving a Prince song. http://www.abajournal.com/magazine/article/copyright_in_the_age_of_youtube/