Hi Bob,
Unfortunately I can't really comment on the decisions the developers of the ssGSEA "2.0" or GSVA algorithms have made, they're a 3rd parties that have adapted the core ssGSEA algorithm that we developed for additional purposes.
That said, the permutation method they are apparently using is one that is effectively derived from the GSEA/GSEA Preranked gene set permutation approach, so rather than the Barbie paper, they're likely intending to refer to the original GSEA PNAS paper
https://www.pnas.org/doi/10.1073/pnas.0506580102This approach was likely adopted to allow ssGSEA to produce additional significance statistics that we do not do, so the ES that ssGSEA produces and the NES that these other methods produce are not directly comparable.
Sorry I couldn't be of more help here, I've reached out to our team members on the algorithm development side, and I'll update you if they have any additional comments.
-Anthony
Anthony S. Castanza, PhD
Curator, Molecular Signatures Database
Mesirov Lab, Department of Medicine
University of California, San Diego