The problem with gambling is, there are so many other readily available alternatives. Yes, DFS could maybe cut him off if he loses "too much", though how we define that is too difficult. If a guy who makes $50k a year loses $50k, that's probably too much. If Mark Zuckerberg does it's not. DFS sites surely can't be expected to know your financial situation.
But anyway, suppose they could. There's always the world's biggest casino: the stock market. Or there are actual casinos. Or there are lottery tickets.
In most gaming jurisdictions, casinos are required to pay for billboards and the like advertising where a problem gambler can get help. (The lotteries, which are state run, never do this, and Wall Street sure as shit doesn't.) I'd have no problem with those sites putting link to Gamblers Anonymous on every page.
But beyond that, I don't think they have responsibility.