I agree It's frustrating that there's no direct description of the supplementary files, but looking at the record it simply says STAR alignment, featureCount, gene-level extraction. The three column files have: geneID geneLength readCount, while the two column files simply have geneID readCount. The two column files also have 91 more genes counted than the three column files (for the few I looked at). I'd guess they may have been aligned by different people, or using slightly different transcriptome versions. Or maybe whoever assembled the submission changed their process while putting the submission together (including or excluding the alignment target length from the file).

This is a good case for simply downloading the raw data and aligning and counting it yourself - especially if you have to analyze the entire data set, given that all the files don't have counts for all the same genes. On the other hand, for a quick analysis you could extract out the counts for the common gene set, but do some QC to make sure the data sets are comparable.