I agree that there is not a huge theological implication one way or another with regard to the exact means by which Jesus was executed. However, I would note that scholars who say Jesus died on a traditional cross do not get the attention of the media. It is only ones who publish provocative (even if dubious) claims who get published. For this reason, you should be quite skeptical of such articles when they show up in the popular media.
I believe that there is a more evidence for crucifixion on a cross-shaped pole than this author implies, although it is likely the "cross" was capital T-shaped rather than the traditional cross.. I would dare to say that he may not have done his homework–either that or he is failing to notice some rather obvious facts. First of all, there is the statement in Psalms 22:16, "they have pierced my hands and my feet." Then there is the striking archaeological evidence of the nail piercing the two ankles of a crucifixion victim which was found in Jerusalem recently. (See below)
Then there is John 20:25 in which Thomas demands to see the nail marks in his hands. So, we have good evidence of nails in the feet (see the figure) and of nails in the hands. That is, unless this author thinks that John, who was actually there at the crucifixion, is incorrect about the use of nails for the crucifixion. Peter also declared publicly that Jesus was nailed to a cross (Acts 2:23). If all that Mr. Samuelsson is saying is that he doubts that the thing to which Jesus was nailed to had a horizontal piece, then I suppose his theory is possible, but not likely. If he denies the nailing, then he is going against the eye-witnesses. He says there is "no explicit references the use of nails." This is clearly not the case. Personally, I am more inclined to believe the statements of the eye witnesses than a scholar, speculating two thousand years later. As for the use of a cross-beam, I will agree that it is not inconceivable that the pole was in fact simply a vertical one, but the evidence for a horizontal beam is more impressive than Samuelsson implies. First of all, there is the fact that Jesus carried the cross-beam to Calvary. Logically, it seems far more likely that he carried the horizontal beam than a vertical one which would have to somehow be put into the ground sufficiently deep to stand up to the crucifixion. A vertical pole sufficiently long to hold an extended body, with the arms above and with length to go into the ground, etc, would have to be at least ten feet and probably more. A five-foot long or so cross beam seems more reasonable. Sameulsson chooses to ignore the church tradition of a cross-beam, but did he do research to discover how early in the Christian literature and art we can find the horizontal piece? It is not inconceivable that the early church could have gotten it wrong, but to simply blow off the traditional picture of the cross as useless information seems to be a bit of a stretch. If Samuelsson believes that the crucifixion instrument was in fact a vertical pole, without a cross-beam, then how does he explain that the early church got it wrong? There is no doubt that the word, rather early on, for cross implied a horizontal cross beam. Sameulsson says that the Greek word is ambiguous. OK, let us say that it is. So, either it was simply a vertical pole, without a horizontal beam or it included a horizontal beam. Given that we know the earliest tradition included a cross-beam, then why does he take as the default position no horizontal beam. I say his claim that there were no nails is extremely dubious. His theory that there was no cross-beam is weak and is certainly not the most likely conclusion of the evidence, but although it is not the most reasonable conclusion, it is not completely ruled out by the evidence. I believe he would be better to say that the traditional idea of a horizontal beam is likely, but not proved.