They do use some more data than that, see my quote.

2.5. Indices of global change

We compared global human population size in the three main phases of facilitation, transition, and the negative r∼ N phase (see Results) to the global temperature anomaly obtained from the HadCRUT.5.0.2.0 ensemble prediction anomaly [56] relative to the 1960–1991 baseline (data available from 1850 to the present).
We hypothesize that the strongest positive relationship between human population size and climate change occurred during the negative phase because of consumption externalities such as increasing natural resource exploitation and loss of biodiversity. This can result from societies in the period of declining r and resources subsequently driving environmental degradation. In contrast, societies in the facilitation phase might have adequate resources to fuel increasing population growth rates.
We also used two additional indices of global change in the analyses to corroborate the results using global temperature anomaly: global ecological footprint measured as the number of Earths required to meet consumption rates [29], and total annual CO2-e emissions (ourworldindata.org).