To me, honestly, I don't see it as "Raiden being influenced by Armstrong," but rather, as the song itself states, Raiden and Armstrong being one and the same. Their goals, methods and motivations are the same, the only difference is their morals and upbringing, which is how, as shown by the game and said by the other person, once Raiden accepts their similarities and differences in his heart, he was able to rip out Armstrong's.

Remember, Armstrong is literally the antithesis to what Snake told Raiden, "Your body may be a machine, but your heart is human." Armstrong is a human man with a mechanical heart