As someone who has never touched a Max Payne game before, I don't think I can offer much, but, from what I can tell, that was a pretty good effort.
I really liked the piano sections with 'sometimes a man with nothing good left to die for' really great, as it felt really close to what I have always thought the Max Payne games were about: a grizzled Noire detective giving an overly dramatic yet undeniably awesome narration in a deeply stylized setting. The rest of the song felt like quite a different tone to that, but I imagine that might have been your goal, as Max Payne 3 seems to be a big leap for the series in a new direction (setting wise), but I never felt like it was out of touch with one another, and I thought it was a good merging of the two. The buildup near the end was also really well done.