The way I see it, most people don't know who Bill Drummond is. Vastly more have never heard of No Music Day. Vastly more still don't care enough about music, however important it is to them, to have to re-examine their relationship with it; or ponder on what they want from it, perhaps listenening to music in alphabetical order for the next twenty-six years.
Bill Drummond is a musician, however, and musicians like attention, on the whole. They also don't realise that not everyone is as serious about it as they are. I don't think that makes him a twat. But it doesn't mean that No Music Day is a good idea, either.
I've not listened to any music today, but I'm sure I will as I see no point in doing otherwise.