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"Studies have shown that about one ton of carbon dioxide is released from every ton of cement produced.”

I was with the author up until that point.

A ton of ~~concrete~~^cement releases a ton of CO2? That doesn't even make sense. I might believe that concrete releases a similar amount of H2O during the curing process, but CO2?

I to was repelled by that. But not because what he is saying is bad chemistry, but because it is stage-1 thinking, as Sowell would put it.
Concrete is a mixture of cement and aggregates such as sand, gravel - and/or, in this case, graphene. The cement is made by heating limestone, producing the endothermic reaction
CaCO₃ —» CaO + CO₂
You can easily see that the mass of CO₂ byproduct will be comparable to the mass of CaO product. The chemistry is good, as far as it goes. But when you add water to the CO, what you are doing is facilitating the reverse, exothermal, reaction
CaO + CO₂ —» CaCO₃
. . . which over time converts the cement back into “limestone” (tho we don’t call it that, but rather, “set concrete” given that sand and gravel have been incorporated before the water was added.
I’m pretty sure I have that right, and the water is effectively a catalyst.
So when you actually use the cement, the CO₂ which you “evilly” added to the atmosphere in the process of making cement gets reabsorbed into the set concrete. No harm, no foul, even from the phoney AGW perspective.
But all that is aside from the point that the claimed properties of concrete with graphene incorporated are quite distinct from those of traditional concrete. Specifically, they claim that the stuff has significant tensile strength. Which is a property considered negligible when designing with traditional concrete. IMHO if nothing else, that property would recommend itself to anyone using concrete structurally in an earthquake zone.
Depending on how significant the tensile strength actually is, it would compete with steel reinforcing or even steel-prestressed design in concrete structures.