The item depicted in the picture is a shendyt. This is still, arguably¹, a type of skirt, and was usually made of linen or imported silk (for richer people). Using the term shendyt in your writing will probably imply having to explain what a shendyt is. It can be defined as a type of skirt — or a wrap around, belted, clothing garment covering the groin area and upper legs — worn by males during the Old Kingdom. Alternatively just use skirt, which with enough context should be understood.
Kilt might be another option, however you would still need to distinguish between the typical tartan kilt and the light ancient Egyptian linen version.
Loincloth doesn't really fit here since a loincloth is only meant to cover the genitals. Note that poorer people in Ancient Egypt might have worn loincloths, so the distinction is quite relevant.
¹ Reason for "arguably": the Oxford Dictionaries definition of skirt implies it is related to female use only; Collins' is less restrictive.