This is a good question, why does it matter if chess is sport or not. I can see two possible reasons which have some ground to stand on:
1. Because a spade is a spade. If you come from a culture where chess is in fact seen as sport, this whole question becomes as pointless as telling anybody "if you think boxing is a sport, just call it a sport". Well, yeah sure I will, because it is. And for the other side it sound to relativistic: can I call my president a king, my cat a dog and my math home work a sport too?
It becomes even harder since definition of "sport" is better found in philosophy of sports journal rather than dictionaries.
2. Because it activities which are classed as sport and are part of sport federation have so much easier to get faster and cheaper access to locals, tournaments, tax reduction, visas for traveling and so on. This would make it easier to start clubs and tournaments.
One could argue that sports get the help from government because they promote health but then again, pro sport are usually a hazard for the health and saying darts, billiards and shooting is so much healthier make the whole issue fuzzy.
I know this has been discussed before, but the threads are old, long, and have become off-topic - as this one will eventually become as well.
So the question - "Is chess a sport?"
My answer? It doesn't really matter - does it?
Now, that may seem apathetic and/or an opinion, but I have a logical foundation behind that. Words are subjective and ever-changing. What is today, isn't tomorrow. We see that more now in the rapidly changing World than we ever have.
And especially US English, there really isn't a governing body that determines definitions of words; it is mostly based on usage. Do you want chess to be a sport? Just call it a sport - forever. If it catches on, it WILL be a sport by definition - if it isn't already.
I'm the type of person who likes things "all neat and tidy." I like standards and classifications, but more importantly? I like to understand the World as it truly is. Whether chess is or isn't a sport today does not mean it will or won't be tomorrow, and that is without the game actually changing whatsoever. All that will have changed is our perception of what "sport" is. So as I said I like standards and classifications, I have to understand things that CANNOT be "neatly classified." What IS or ISN'T a sport is one of those things - and belongs in courtrooms, where they purely talk about nothing but for the sole purpose to hear themselves talk.
So I say whether or not chess is a sport - is irrelevant. Just play and enjoy it.