You might be happy to hear that the author of the article founded a company (Terraform Industries) that is working on making carbon sequestration and synthetic fuels economically viable.
Money put into synthetic hydrocarbon production is extremely premature when we don't have enough renewable generating capacity yet to displace current CO2 emissions.
I'd word it as "Developing negative carbon emission industry and economy on Earth will almost certainly lead to better ways of doing things on the Mars" as in the two questions aren't different enough to phrase them as a "this one" or "that one". Solving one without solving at least a significant portion of the other doesn't seem possible and I don't see the desire for either shrinking as time goes on.
There is limited evidence large populations are willing to incur pain to solve the climate crisis. To the degree money is spent, it’s politicised and inefficient. The necessity of survival simply isn’t there here. It would be on Mars.
It would help, some, for it to be actually possible for a Mars colony to exist, and then maybe to survive at all. But there is thus far no reason to expect that. Certainly not by relying on Starship/Superheavy, which is so far from adequate it is comical.
Starship might be adequate to keep a small moon base operating. That would be an achievement.
Necessity is the mother of invention.