Like other expressions, economic categories reflect reality, and the term royalty isn't an exception.
Michiel de Vaa’s Etymological Dictionary of Latin and the Other Italic Languages (Brill, 2008) has no entry for royalty or its lemma. See his near-neighbor entry (Vaa, pp. 517-518): rego ("to direct, guide, govern"), but the listed cognates don't refer to payments or other economics allusions.
The Oxford English Dictionary, an erudite arbiter of the English language, includes several meanings for royalty (noun (plural royalties)), and attributes its origin from Old French roialté, from roial (regal):
“The sense ‘royal right (especially over minerals)’ (late 15th century) developed into the sense ‘payment made by a mineral producer to the site owner’ (mid-19th century), which was then transferred to payments for the use of patents, trademarks, and copyrighted materials.”
See the Oxford English Dictionary. Cite: “royalty, n.”