This is the 9507th most frequent Polish word.
wileńskiemu
"Wileńskiemu" means "Vilnius-related" or "pertaining to Vilnius" in the dative case, masculine singular.
In this sentence, 'wileńskiemu' describes the writer, showing association with Vilnius, and is in dative form to indicate the recipient of the dedication.
Książka była zadedykowana wileńskiemu pisarzowi.
The book was dedicated to a Vilnius writer.
Here, 'wileńskiemu' is in dative case modifying 'ambasadorowi', identifying the ambassador associated with Vilnius, as the indirect object receiving the letter.
Przekazałem wileńskiemu ambasadorowi list.
I handed a letter to the Vilnius ambassador.
The word 'wileńskiemu' is used here as a dative adjective referring to a male guide associated with Vilnius.