How can every ton of CO2 cost 3 square meters of summer sea ice per year - quantitatively?
First lets take the question at face value and do the simple comparison. I will take the years 1979 and 2016 as arbitrary example, over a 37 year period - the longest for which accurate data are available. During that time the minimum extent of Arctic sea ice, defined as the area of Ocean with at least 15% of sea ice (as determined by satellite) decreased from 6.93 to 4.14 million square kilometers. That is, a decrease of 2.79 M Km2. The actual ice loss was much greater because of ice thinning, but that is incidental to the question. During the same period the CO2 emissions by the USA increased by about 160 M tonnes. So on the face of it, assuming a direct linear relationship, 1 tonne of emitted carbon from America results in an average of 0.029 km2 reduction in ice, or about 3 hectares (Not Km2! let's get the units correct!).

Of course, as every scientist knows, a correlation - even a good correlation, doesn't necessarily imply causation. In this case it would be correct to say that every tonne of burned coal eventually contributes towards the loss of Arctic ice, but the whole process is much more complex, with an abundance of other contributing factors, feedback processes, and non-linear relationships coming into play. Among these complicating factors are Arctic ice thinning, changing Arctic albedo, changing ocean-scale oscillations, Other country emissions, inter-annual changes in thermal inertia (land, ice, sea and atmosphere), and high-level atmospheric chemistry (volcanic gasses, aerosols, etc.). So although there is an element of truth in your article, it would be naive to imply a direct relationship.

To keep an eye on how the Arctic ice is responding to climate change I highly recommend 
http://nsidc.org/arcticseaicenews/