Hi, László. With only a quick read of the paper, I'd say that a few elements certainly could be added to Béla III's profile. The usefulness for genealogy comparisons will vary.
I believe we'd have to ignore the autosomal DNA STR information. Short tandem repeats on the autosomes are typically tested for forensic/identification purposes (e.g., paternity, immigration, criminal investigations) but are not routinely tested by any of the largest direct-to-consumer companies for genealogical purposes. And because that type of testing is generally not for public consumption, there are no public databases that I'm aware of with which to compare actual STR values.
The yDNA prediction of an R1a haplogroup is likely valid and should probably be added to the profile for reference. The study didn't perform a SNP test on the Y-chromosome (which often isn't practical or even possible on ancient remains), but used STR results and Whit Athey's (a WikiTreer, by the way) predictor to arrive at the R1a value; this would be equivalent to a L146+/M420+ SNP result. Whit's predictor algorithm has always been solid, but can only go so deep. R1a is useful to know, but it's far too common and far to high in the R clade to be used for genealogical matching. A disagreement in a high-level subclade--for example in skeletons I/3G, I/4H, II/53, and II/55 in the study--is evidence of no shared paternal lineage in any meaningful timeframe. A mismatch can disprove, but a match only at that high level isn't probative.
The Y-STR markers tested are a bit unusual. They tested a total of 17, and I didn't see an explanation as to why those 17 were chosen. For genealogical purposes by far the lion's share of yDNA testing is done by FTDNA, and without double-checking myself I believe 10 of the markers would appear in FTDNA's Panel 1 (12-marker test); 3 would be in Panel 2 (25-marker test); 3 would be in Panel 3 (37-marker test); and 1 would be in Panel 5 (111-marker test). The end result, in my opinion, is that even if current yDNA testers show the same values at those specific 17 STR markers, it would be inconclusive genealogically and unusable as evidence of descendancy. A significantly greater number of marker results would be needed for that.
For mtDNA, the H1b mitochondrial haplogroup designation for Béla is useful information and can be evidence to disprove a maternal-line match, but too broad to be evidence for a match. The study uses only SNP comparisons against the revised Cambridge Reference Sequence (rCRS), not the Reconstructed Sapiens Reference Sequence (RSRS) which is becoming more common.
Similar to the Y-STR testing, the mtDNA has me scratching my head a bit. And maybe someone more knowledgeable can offer some insight. The study states that three hypervariable regions were tested, HVR1, HVR2, and HVR3, and that testing included sequenced ranges from bp 16009 through 16569 and 1 through 594. I'm familiar with an HVR1 and HVR2 only, and these are sequenced as HVR1, 16024 through 16569 (546 base pairs), and HVR2 from 1 through 576. I have to believe that the handful of base pairs before HVR1 and after HVR2 are what's being referred to as HVR3 in the study. In my experience, and the way FTDNA reports, HVR1/2 are as I described, and all other base pairs in the mitochondrion are part of the "Coding Region."
Regardless--and with the caveat that some do--I seldom consider only matching results in HVR1 and HVR2 as genealogical evidence; I feel it takes a full-sequence test for that. Unless the resultant haplogroup is quite rare, there simply isn't enough distinguishing data in HVR1/2 to serve as evidence for genealogical matching. Referencing FTDNA again, in generalities (not considering the rarity or commonness of a set of results) they state that an exact match in both HVR1 and HVR2 has about a 50% chance of indicating a common ancestor within 28 generations...or about 700 years. They won't refine that 50% confidence level any tighter at that level of testing. With an exact match in a full-sequence test, FTDNA will go to a 95% confidence level of a shared maternal ancestor within 22 generations. Genealogical matching with HVR1 and HVR2 data only is essentially the same, IMO, as claiming valid yDNA evidence with only a 12-marker STR panel tested.
More than you wanted, I know...and all are my opinions, not WikiTree's. But it touched on a couple of soapbox issues of mine. :-) Bottom line, if I were the profile manager for Béla III I'd definitely want to add information in a section of the biography about this study by Olasz, Seidenberg, Hummel, et al., and I'd want to state the predicted yDNA and mtDNA haplogroups of R1a and H1b. Fascinating stuff, all around.