Thankfully this study actually listed the SNP in question so we don't need to figure out which ISOGG tree they used, so we don't need to pursue the endless alphabet soup that is the ISOGG tree. The SNP they reference is M412, which is phyloequivalent to L51, S167, PF6536, MF39636, etc. The study you reference is about modern distribution, which is very different from ancient distribution, this can be seen in more than just haplogroup R1b, for example certain clades of haplogroup I2 were found in paleolithic samples in Scandinavia, yet I2 is relatively uncommon in Scandinavia, it is overshadowed by R1b, R1a and I1. I2 was really quite abundant in the very ancient samples across Europe, yet it was clearly replaced by other lineages during a very obvious rapid growth of R1b, R1a and I1 in the Bronze Age timeframe.
R-L51 (aka M412) was found in the Samara region with the Khvalynsk (5th millennium BC)
https://indo-european.eu/2018/05/hap...-4250-4000-bc/
Again, this is found in a culture that is contemporaneous/subsequent to cultures of the Pontic-Caspian steppe such as Repin, Khvalynsk and Yamnaya. The samples they have found an related L23 clades in the Samara region and Pontic-Steppe related cultures is very telling. As this is quite some time before the testing of modern Y-chromosome distribution in modern Iranians that you cite. These ancient samples fit with the timing of the eventual rise of Proto-Indo-Europeans who eventually spread westward and eastward (with the Indo-Iranian group branching off toward Iran and India).
https://indo-european.eu/2018/04/ear...ng-migrations/
If we look at YFull, they list that R-L51 formed 6100 years before present and diversified 5700 ybp. It's descending branches notably R-L52 and R-S1200, R-U106 and R-Z2118 have wide ranges due to proliferation of these lineages. What are the modern terminal SNPs of these Iranian R-L51/M412s? Were they tested for anything further than M412? Are they M412*? An ancient sample is quite a bit more telling than the modern distribution.
The paper you cite even states and the go on to say
It would seem logical that Proto-Iranians carrying various R haplogroups, namely clades belonging to the L51 branch and various R1a branches would have spread this lineage in various directions with the migrations and movements of Cimmerians, Sarmatians, Scythians, Alans, Medes, Persians, Bactrians, Parthians, etc. and more specifically the Iranian-speaking populations who moved into the Iranian plateau would be responsible for introducing R-L51/M412 into the area introducing it as a lineage from which a portion of the modern Iranian population descends from.