Methane has a short half-life in the atmosphere, so its cumulative effect after a few decades is close to CO2 unless you're constantly outputting more, and that's assuming you're not burning it.
In the case where you're making methane from atmospheric CO2 and then burning it, it's just returning the same CO2 back, which per the article is carbon neutral.
There's a big difference in scale between "burning hydrocarbons to heat and power much of the world" (which includes leakage from fossil fuel drilling) and "we make some methane to be almost completely consumed and there are some leaks".
In the case where you're making methane from atmospheric CO2 and then burning it, it's just returning the same CO2 back, which per the article is carbon neutral.