To summarize, the Symphonic Game Music Concerts were the first concerts outside of Japan dedicated to video game music. They were held at the Gewandhaus concert hall from 2003 to 2007 as part of the annual Games Convention in Leipzig, Germany. I have spent much of this month searching for any video or audio recordings of the events to preseve them for posterity.
At last, I came across several videos taken at the concerts. Or more accurately, I came across one video I could watch and several videos I couldn't. This is an incomplete recording of the famous "Dancing Mad" from Final Fantasy VI, performed at the Fourth Symphonic Game Music Concert. Thisisgame, a Korean gaming news outlet, (presumably) recorded and uploaded the video to their website, but it is thanks to the Otaku no Tokyo channel on YouTube that we are able to view it.
I have already taken the liberty of uploading it to the Internet Archive for safekeeping.
The rest of the footage is on Thisisgame.com and, at least on my end, the videos won't load. I will post links to the remaining perfomances covered by the website.
Third Symphonic Game Music Concert (August 17, 2005) Donkey Kong
If I were to hazard a guess, I would assume that the videos in the articles were Flash-embedded. Unfortunately, I don't know if there's a way to view them anyway, now that Flash is unsupported.