Second, we need to think about the context of the "immediate loss" kicks. In a penalty shootout, each team gets to pick its five best shooters. If the contest is still tied after five kicks apiece, the shootout goes to "sudden death"—if the first team makes its kick, the second team has to score or it will lose the game. In this sudden death phase, each squad must deploy its lesser shooters, the preferred five having already been used in the first phase of the shootout. It's in these situations—when less-skilled players are likely to be shooting—that many of the "immediate loss" kicks happen.
Suppose the score is tied after five kicks each. The first team's sixth kick will never be an "immediate win" or an "immediate loss" kick—it either takes the lead or preserves the tie. The second team's sixth kick, on the other hand, will always be an "immediate win" or "immediate loss" kick. But it will be an "immediate loss" kick much more often than an "immediate win" kick, because the first team will have scored on its previous kick much more often than it will have missed. The "immediate loss" category, then, will almost certainly carry a larger proportion of worse players than the "immediate win" group. That means we should expect worse performance on "immediate loss" kicks even if stress plays no role at all.
How significant is this factor? I don't really know for sure. My gut feeling is that it's big enough to explain the statistical significance of the small "immediate win" improvement, but not enough to negate the larger "immediate loss" difference the studies found.
It's also worth noting that even though the results in these reports were reported as statistically significant, they're based on fairly small samples. The Savage/Torgler study was based on only 49 "immediate loss" kicks, meaning the "choking" conclusion is based on a mere handful of extra misses.
In search of a larger sample, I was led by Google Scholar to this study by Thomas J. Dohmen. Dohmen, who looked at the 40-year history of in-game penalty kicks in Germany's Bundesliga, found one situation that was statistically significant: home kickers were more likely to "miss by choking." (Dohmen's definition of choking: missing the net or hitting the posts or crossbar.) The suggestion here is that the expectations of the home crowd stress the kicker to the extent that he's more likely to miss completely.
The finding was based on 3,619 penalty kicks, about 10 times as many as the other studies. Still, the narrow definition of "choke" meant that there were only 59 such misses by the visiting teams. If you took 15 chokes by home teams and handed them to visiting teams—that's one choke every three years—the effect would disappear. And, of course, there's the more obvious criticism: If playing at home is so stressful, how do you explain home field advantage?
So: Three studies, all of which claim to have confirmation that penalty kickers choke. Still, I'm skeptical that Asamoah Gyan choked when he missed that kick for Ghana. And if some poor Spanish or Dutch player botches a penalty kick on Sunday, I won't be calling him a choker either. If you miss a kick in the World Cup final, though, I'm not sure that's much of a comfort.