Loki is clever enough to see those as statements and not questions, and tickled enough by the distinction to humour the mortal for now. It seems he has some wits to him, more so than the simplicity of Thor who would have thought deeply and then asked as he was requested to do without trying to wiggle around the requirements.

"You know who I am, my name and title have been mentioned in your presence more than once. As for what I am, I am a Jotnar. A frost giant, in the tongue of you mortals. And the eldest child of Laufey-King of Jotunheim."

Though, as a fyri, not eligible to take that throne when Laufey died, that would go to the second son and heir, Helblindi.