Looks like a mod.
Nintendo never released any official video recording devices or TV-out for Nintendo DS/DSi/3DS, so it's either you mod the console, you film with a camera (or a cellphone, or a webcam, you get the idea) or you use an emulator. Unless you're an employee of either Nintendo or some gaming websites (they have officially modded consoles from what I hear) , there are no other options.
I ended up buying an unofficially modded 3DS with a capture card after attempting to record footage from my 3DS XL without modding. Audio capture is obviously very easy, but video capture is a pain when you use a camera, a cellphone etc:
- First of all, the recording device you will use must allow to disable autofocus and automatic color correction, otherwise the device will freak out every time the screen goes black for a second: basically, every time you'll go through a door in Pokémon, you'll get a few seconds of blurriness and/or extra brightness when the image will come back on. It's very hard to find a device that allows disabling both nowadays.
- Second, you'll need to find (or build) something stable enough to hold your recording device in place while you record. Depending on what you find to hold your recording device, you might need to do the same for the console itself.
- And finally, if you want your videos to look good, avoid using the touch screen as much as possible (unless you hold your stylus in a very uncomfortable way, your hand will more probably than not cover half of your lower screen) , and above all, you absolutely can't move your console when you play, and it's very hard to do with a handheld. I tried playing Pokémon like this and it sucked, I can't even imagine recording an action game with such a setup.
This was from my experience, from what I see on Youtube some people have better luck than me.
EDIT: I forgot another thing I've seen on the internet: there's some sort of a camera attachment for the DS (you basically wrap it around the top screen of the DS), it doesn't require modding, but the colours are darker around the edges in the recorded footage and you only can record the top screen. I don't think these are available anymore, but just wanted to let you know.