The similar soundtrack isn't a coincidence. Harry Gregson-Williams composed the score for both The Rock and later MGS games. And yes, you can definitely see Michael Bay's influence in Kojima's cutscenes.

You could as well say that it ripped off The Rock. A group of ex-soldier terrorists takes over a former base and steals a weapon of mass destruction. The good guys are a badass soldier and an inexperienced scientist. The hero gets imprisoned and escapes using his wit. The story ends with one of the bad guys being…

Kojima didn't rip it off, he named the protagonist after Snake Plissken as an homage and used a similar story structure, which by that time has been copied to death in countless B movies.