The political variable is defined for three categories: "left-wing", "right-wing", and "otherwise".
If the researcher wanted to be completely agnostic, and let the data speak the most, she would include a dummy for each category (or two categories if a constant is used). For example, the model could include a constant, a dummy equal to 1 if the government is "right-wing", and a dummy equal to 1 if the government is "otherwise". The base category, reflected by the constant, would be that the government is "left-wing". In this case, the value of the constant reflects the effect of a "left-wing" government on GDP, whereas each dummy's coefficient indicates the difference of the political ideology of the government on GDP compared with the base category, i.e. the "left-wing" government. This approach allows for political ideologies to have any effect on GDP. For example, it could be that the third category - "otherwise" - has exactly the same effect that a "left-wing" government. This is the case when it's coefficient is zero.
In the paper you mention, the author is assuming that the differential effect of political ideology on GDP between the three categories is the same. This is, that a ceteris paribus change in political ideology from "left-wing" to "otherwise", and a ceteris paribus change in political ideology from "otherwise" to "right-wing" has exactly the same effect on GDP. Even more, she is assuming that this effect has a certain order ("left-wing", "otherwise", "right-wing"). In effect, this assumption is obtained from adding restrictions on the coefficients in the agnostic model (more precisely, is assuming in the agnostic model that the coefficient in "right-wing" dummy is twice the coefficient in the "otherwise" dummy). As such, it is a more limited approach. From your question we don't whether that decision is based on a pre-test or not, but to me seems to be quite a restrictive approach, and probably unnecessary if enough degrees of freedom are available.