In the rock cycle, the thing that determines the type of a rock is the way the rock was formed. Igneous rocks are formed by the cooling and solidifying of molten rock (magma or lava), sedimentary rock is formed by deposition of sediments which are either compacted or cemented together, and metamorphic rock is formed when other rocks are subjected to extreme pressure and/or heat that is not enough to actually melt the rock. The heat and/or pressure can deform the rock and also cause different minerals to form, or else change the shape and distribution of existing minerals.
In the determination of whether a rock’s type is igneous, sedimentary, or metamorphic, it doesn’t matter what knd of rock it came from. It only matters how it was made. The rock in the question is igneous rock, so it had to solidify from molten rock. To become molten, the original sedimentary rock had to melt. Once molten, of course, the structure of the previously existing rock would disappear. The process that would transform a sedimentary rock, or any other rock, into an igneous rock, then, is melting or, to be more specific, melting followed by cooling and solidifying.