Reading the original story (
http://www.democratandchronicle.com/...ruff/18168767/), it doesn't seem like Vanek was involved with any money laundering at all (especially since the whole point of laundering money is to hide the true source of the money).
It looks like all he did was place bets with the illegal bookmaker and lost a considerable amount of money, which he, at least partially, paid off with one of his cheques from the Islanders. Then, the bookmaker laundered the money and was caught doing it. One of the pieces of evidence was the cheque in question -- which is likely why Vanek was called to testify in front of the Grand Jury.
I don't believe Vanek was paying off anyone else's debts. The reason the story uses the term "the bettor" is because no one has confirmed that it was, in fact, Vanek who paid with the cheque. All they know is that "the bettor" paid off his losses with a $230,000 cheque from the Islanders and that Vanek has admitted involvement with these bookies. So, they're basically putting two and two together and assuming that Vanek is "the bettor".
As far as I can tell, the New York State gambling laws are all set up to punish those who operate illegal gambling operations and not the patrons of the illegal gambling operations. Under New York State law, it doesn't appear that Vanek has committed any crimes (unless he was involved in actually operating the bookmaking operation, and there doesn't appear to be any indication that he was).
This seems to be more a case of Ian McLaren badly misreading the original story and writing his story based on that misreading than anything else.