So by this definition any system that is not widely practised as a sport is not a martial art but anything involving fighting is, as long as it is widely practised as a sport. Hmm! That's strange. I no longer practise a martial art by this definition.
Now 'Self Defence' is a martial art according to this definition but 'self defence' doesn't actually exist. Nobody from a self defence background has ever rocked up to the UFC as far as I'm aware.
I was under the impression that self defence was the legal term used to justify the violence your perpetrated in defending yourself, your family and friends or your property. Interesting that it is now a bone fide martial art. For those who have never seen 'real' self defence in action, here is a bit from the self defence world championships.