Many legislatures through their election laws delegate a lot of the responsibility for the manner of the election to subordinate bodies. I pointed out the law in Georgia, where the legislature delegated choosing the place of election to the local county executives.
There are even instances where the legislature gave the power to enact election law, without realizing it.
Under Pennsylvania's Emergency Management Services Code, the Governor is empowered to declare states of emergency and exercise broad authority, including issuing executive orders with the force of law.
Maybe they missed that last part about the Governors emergency powers, giving him legislative powers. And as such, the governor became part of that states legislature for the purpose of enacting voting laws.
When they say legislature, they clearly are talking about the entire state government to include the legislature, governor and state courts. The founding fathers believed in checks and balances.