Thank you ever so much for telling me about Shibuya-Kei. I got a few samples and I am loving it! Although it is not really like the song I mentioned, it is absolutely outstanding. It is like jazz musiciants trying to play pop :-)
I still don't know how to describe the track I mentioned in the original post. I hope I will not offend anyone by saying that it is like A Japanese version of country and western played in a French restaurant (saxophones, violins, clean electric guitar sound), almost like dinner jazz with natural minor harmonies. I appologise, I do not write essays about music, so I could not really describe it well.