OK even though making that kinda puzzle is part of my job, I cannot figure this one out, so I will lay down here all I have found in the hopes that we can figure it out together, classic-ARG-style.
These are the main clues given explicitly. It's fair to assume that the first solution can be guessed from those two things alone.
Gramophone sequence: 183728725
Video link: https://www.youtube.com/watch?v=vb-TwWvNk0k&list=PLF70Y7efqrYM&index=1 (Cell Block Tango)
Extra oddities I've found; may or may not be relevant to this first answer.
Code compiled from the character sheets: 12345
HTML code on the website seems to imply the existence of an 8th page (one more after the gramophone) → solution page?
Is the sequence the ID of an ArtFight character or attack? → no
Is the sequence ciphered? → Unlikely. Most of the common ciphers give me nothing usable. A1Z26 outputs AHCGBHGBE. Even putting that through secondary ciphers doesn't give anything obvious (best is NUPTOUTOR from a rot13).
It is not a factorial nor square number. Maybe some operation on it might reveal something?
The song list numbers through it (2 shots, 6 women, 10 times, 17 spread eagle). Not sure if useful.
The song is from the musical Chicago, which came out in 1975, adapted from a 1926 play. More numbers, not sure what to do with them.
Cell Block Tango... CBT? Likely irrelevant.
Anything special about the musical? The city?
How does the sequence relate to the video?
Is the sequence a series of NumPad scrub commands? → gibberish results
Is the sequence meant to be used on the playlist tracks?
first word of tracks? → "cell beneath terrible bell not beneath bell not mikky" ....gibberish?
Maybe the 1st answer is located on that 8th page. → How to access it? Just URL guessing?
IMO, the sequence has to be used to retrieve something from the Cell Block Tango video, so that's the direction I'll focus on again tomorrow.