What are the purposes of doing a research study on how dialects impact gender?

As Joe Devney said, depends on the study, but I have a fair guess.

That would be gender, presumably, as in grammatical gender, in those languages that have them. The wording would then presumably be something more like how does assignment of entities to particular genders vary from one dialect to another within the same language.

Dialects are linguistics’ natural laboratory: you have a common starting point for the dialects that’s quite well understood, even by laypeople—they can work out how the dialects relate to each other and to the common core of the language without much trouble. So the variation in how different dialects treat the same phenomenon can be mapped out straightforwardly. Because the dialects have diverged recently enough, those changes can usually be made sense of easily, compared to changes between different languages.

So the variation in gender assignment within a language, between different dialects, will have a common starting point—in Modern Greek dialect, say, Ancient Greek; and you can make sense of the variation between dialects, because there’s much less variation to trace than, say, the variation between French and Russian.

The purposes of such a research study would be the same as the purposes for any research study on how entities are assigned to gender; the results would just be much more tractable.