"Kālua is a traditional Hawaiian cooking method that utilizes an imu, a type of underground oven. The word kālua, which literally means "to cook in an underground oven", may also be used to describe the food cooked in this manner, such as kālua pig or kālua turkey, which are commonly served at luau feasts. Luau, in Hawaiian is actually the name of the taro leaf, which when young and small after being steamed for a few hours resembles cooked spinach. The traditional luau was eaten on the floor over lauhala (leaves of the hala tree were weaved together) mats. "
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Well, in Hawai'i that is what it is called - kālua pig. This is not just a translation or an explanation of what the sentences are. It is what is said in Hawaiian with its equivalent in English + vice versa. Besides, kālua implies baked in a ground oven or in a way that mimics it. It is not the same as bake meaning baking a cake. Technically, we could also include pulled pork since that it what it is called on the continent.
In Hawaiian, nearly all common nouns need a ka'i , basically what is known as an "article" in English. ke/ke are just two ka'i but they don't always have to tramslate to "the," sometimes they are just there becauase they're req'd. Don't get too hung up on thinking every Hawaiian word has to have an Englsih equivalent. But, to answer your question, yes, your translation says what you wrote.