As I thought, your friendly probably is getting its backgrounds from Just Dance Now website. In the page I linked you before you found a lot or URLs from Just Dance Now, and the syntax for getting the backgrounds is something like
http://hls.justdancenow.com/(songname)_(...number).ts
Unfortunately, to make these URLs work you have to play the song at least once in order to set a cookie in your browser and allow you to download the videos. Since most of songs are premium, you'll need a VIP pass to access these songs. In the example below I'll be using Movement is Happiness as example (as far as I know, this song is free since JD Now release).
First off, you should go to
http://justdancenow.com to load the song once and set the required cookie, so, go to the game's page, click "Play" and choose the option to continue without pairing a smartphone. Now you are in the song select screen, select the desired song -- in this example I'll be using Movement is Happiness since it's free and doesn't require a VIP pass-- and click play (this should set the cookie in your browser -- remember that if you close your browser, you'll need to repeat this step). Now I can freely download the videos used in that song.
Looking at the page I linked before, you should see that song name for Movement is Happiness is
FindYourMove and that the song code is
6f4d3f5b. In this page we can also confirm this song is split in 21 parts (each part is rougly 11 seconds), so part number can be anything between 0 and 21. Quality is related to video size (similar to the video quality setting we have in YouTube) and the valid values are
1m (roughly 360p),
2m (roughly 480p) and
4m (roughly 720p). Now we can construct the full URLs to get the video (remember, in this example I'm using Movement is Happiness as example and I'm getting the 720p version -- song name must be lowercase):
Code:
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00000.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00001.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00002.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00003.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00004.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00005.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00006.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00007.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00008.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00009.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00010.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00011.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00012.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00013.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00014.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00015.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00016.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00017.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00018.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00019.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00020.ts
http://hls.justdancenow.com/findyourmove_6f4d3f5b/4m00021.ts
These files are standard H.264 video with AAC audio so you should be able to join them with almost any video editing software, in order to get the full video with the dancer and the background. The main video is split in several parts because of adaptive streaming: the game will mix files from different quality during gameplay in order to match your connection speeds. It may also worth noting you can gest an M3U8 playlist pointing to all parts by ommiting the part number and replacing the .ts extension with .m3u8 (in the example above that would be
http://hls.justdancenow.com/findyourmove...5b/4m.m3u8 but you can change 4m with 1m or 2m too to get the other sizes)
About errors, you can get two different messages when trying to access the files, the first one is a XML response saying "AccessDenied", that means your URL is incorrect, check for typo errors, etc. However, if you get "An error occurred while processing your request" then your URL is correct but the cookie that allow access isn't present in your browser. Just start the desired song in the game and the cookie will be set, allowing you to download the files...