Leinster, Murray. "The Other World"
Summary: Ancient Egyptian priests discovered a parallel uninhabited Earth and sustain themselves by surreptitiously looting ours for merchandise and slaves. Allohistorical content is negligible.
Published: In 6 Great Short Novels of Science Fiction (ed. Groff Conklin), Dell 1954; and Robert Adams' Book of Alternate Worlds (eds. Robert Adams, Martin H. Greenberg, and Pamela Crippen Adams), q.v.