I'd take FAR issue more with the fact that the authors appear to have mixed up correlation and causation. e.g. the fact that, say, international conflict causes a bad economy and populism (the "war is bad" theory) appears to have flown completely under the radars of Manuel Funke, Moritz Schularick and Christoph Trebesch.
Also the fact that GDP is well known to be a shitty measure of well being for the average person. Nonetheless, it is a pretty good measure of how things are going for that particular country's oligarchy (the targets of those populists). There's also a strong causal relationship between using GDP as a measure and getting published in the AEA.
As a side-note, it's interesting to see that their data shows that populists generally stay in power twice as long as none-populists and they are often removed from office in "non-regular ways".
According to today’s workhorse definition, populism is defined as a political style centered on the supposed struggle of “people vs. the establishment” (Mudde 2004). Populists place the narrative of “people vs. elites” at the center of their political agenda and then claim to be the sole representative of “the people.” This definition has become increasingly dominant, and is now also widely used by economists (see Section 2, and the recent survey paper by Guriev and Papaioannou, 2020). Populist leaders claim to represent the “true, common people” against the dishonest “elites,” thus separating society into two seemingly homogeneous and antagonistic groups.