In the Limitations and Directions for Future Research, it also note that right-wing ideologies tend to be more prosocial toward ingroup members than left-wing, which the economic games that the study uses may have a bias against. That would contradict the simplistic conclusion that the prosocial behavior is unconditional.
That supports the original comment, which asserted that right-wingers often only experience empathy for the ingroup while left-wingers also experience it for the outgroup:
> We have seen this pattern repeated with numerous people who share Adams' political opinions, in that this level of empathy only seems to arrive once they themselves go through a similar experience. People who have that empathy without the need of that direct experience tend to have different politics.
Personal experience can definitively help to form identity, but it can also be completely abstract and arbitrary. In many situations there are just an abstract proxy of an implied shared experience that never happened.
Left and right-wing voters also divide the in-group and out-group categories differently, which adds an other dimension to studies looking at empathy towards in-group vs out-group based on political alignment, and they will definitively differ when looking across borders and culture. The in-group of a left voter in the US may be the in-group of a right voter in Germany.