What's the tune that starts at about 4:27?
That's the boss theme from Streets of Rage.
I couldn't recognize most of the music, but I was pleasantly surprised when I heard Stone Man's theme.
I didn't recognize much of it either. I think that there was some Street Fighter in there, and nobody can mistake the Pac-Man jingle. There was some Streets of Rage, Mega Man (Stone Man and Cut Man), the Capcom logo jingle, and the hurry up jingle from Super Mario Bros.
I looked for a complete list of songs used in this video, but I couldn't find one.