I've seen forums get flooded for no other apparent rationale than some random skiddie had nothing better to do for an hour or two than irritate the admins. It being not worth anyone's time to break isn't actually a feature, but it being relatively easy for anyone with time to waste on it is a flaw.
Chess is even a particularly ironic implementation because it was one of the first traditionally human passtimes where computers excelled.
A site can have a CAPTCHA that's so bad it's not actually a CAPTCHA even if no one bothers to attack it. My hidden forum could require a user to sum one thousand integers before seeing any posts. I probably wouldn't attract any spammers (because no one would join to read their spam), but that doesn't mean the so-called CAPTCHA is beyond reproach.
http://en.lichess.org/captcha/78pkfjgz?solution=e5+e4 which returns 1 or 0.
So the brute force captcha solution is to go through 8^4 (~4k) get requests, which you could code in five minutes and execute in a minute.
There are easier to implement unique captchas, than chess.
Another way to look at it is like the entire collection of CAPTCHAs on the Internet is really just one big CAPTCHA library, which tests a subset of "human" abilities. The larger the subset, the more difficult it will be to circumvent. Relying on one or two special abilities makes it easier for a machine to emulate those behaviors and gain access. I hope that clarifies the point I was making.
Custom captchas are probably a great use of this.
You raise a good point about making captchas that target your target audience in that they aren't really designed to keep out bots, but humans who wouldn't fit in. This looks very much like that sort of captcha.
You have what, 11 pieces, they can move into 64 positions each (at most, much less in reality). That means a computer must brute force 64*11 = 704 attempts.
In other words, no time at all to bruteforce this once you've read the grid. Reading the grid in itself is rather trivial since you only have a small number of clearly distinguishable pieces to recognise.
So after an afternoon of coding, I could have a computer that solves this CAPTCHA in a few seconds. As a human I need more than 30 seconds just to read the current situation on the board.