Why was this question - my first on this site but far from my first on SE; I certainly don't see how it is overly broad - closed, just when it had begun accruing useful responses? A question requiring broad rather than deep knowledge does not necessarily fail to "focus on one problem only".
How ought it to be improved? The point is that I cannot ask a series of questions like, 'Are there any full-time players of Scrabble?', because if I knew which boardgames to ask that question about then in most cases I would already have the answer.
The only logic provided for what I presume was one of the closure votes seems absurd (if one wants to claim there exist 'many games' with full-time professionals that few have ever heard of - when even the most popular games, short of chess/Go/poker, struggle to sustain full-time professionals - the burden of proof for such an odd claim is clearly upon them). No logic whatsoever for the other votes. So nothing to go on to improve the question really.