Well, it seems like when they say "Homeric Greek", they really mean just that.
Are there any other authors besides Homer who wrote in Homeric Greek?
No, there are no other known authors who wrote in Homeric Greek as a literary style after the time of Homer. Homeric Greek was a specific dialect and literary style that was used by Homer and his contemporaries during the early Archaic period of ancient Greece, around the 8th century BC.
After Homer's time, the Greek language went through a series of changes, and literary styles evolved. Other ancient Greek authors, such as Hesiod, Pindar, and Aeschylus, wrote in different dialects of Greek that were used in their time, but they did not imitate or adopt the Homeric style.
It's worth noting that later authors, particularly during the Hellenistic period, did study and imitate the works of Homer, and his influence can be seen in various literary genres, such as epic poetry and historical writing. However, they did not write in Homeric Greek as a distinct literary style.