Why is "their" italicized? [closed]

It is done to make a clear distinction between the two 'their's in the sentence.

The sentence can easily be split into two halves:

Some elections are held in friendly client states to legitimize their rulers and regimes

and

... others are held in disfavored or enemy countries to legitimize their political systems.

In the first half, 'their' refers to the friendly client states.

In the second half there might be confusion - does 'their' refer to the friendly client states or to the disfavored or enemy countries?

Using italics for the second 'their' indicates that it refers to the disfavored or enemy states.