The calculation that matters is how much money a family has left after they pay for their insurance. Look at the families the article gives the numbers for (I'll assume the numbers in the article are correct):
|Family||Actual Income||Premiums||Net Income||Lower Income||Lower Premiums||Lower Net Income||Savings|
So in two out of three cases the Times describes, the families either have more income after insurance (OKC), or effectively the same amount (NH) that they would have if they made the lower incomes described in the article (ignoring the effects of income tax). At least one of the other families is likely in a similar position (the Montana bakery owners, who would pay $1,500 more a year if their income rose by some unknown amount, which is likely more than $1,500). Most families will have more net income if they make the higher income, even with the higher premiums. In other words, the subsidies are doing what they're supposed to, making the insurance more affordable for those with lower incomes. That they're not helping families who don't qualify for them seems beside the point.
What the article is really about is how for some people ACA insurance will cost more than they currently pay, and it mixes in this mostly inaccurate attack on the subsidies. But even here the article falls down because it doesn't compare all the old and new health-care costs of the families. Premiums are only one part of those expenses: there are co-pays for office visits, medicines to purchase, and so on. Granted, it's not easy to calculate that. You'd need a lot more data than are presented in this article, but that's why this health issuance stuff is hard.
Who's spending more or less on health care because of the ACA? We know as little at the end of the article as we do at the beginning.