1580s, "to rule in a despotic or arrogant manner," from Dutch domineren "to rule, play the master; to feast" (16c.), from French dominer, from Latin dominari "to rule, 'lord' it over," from dominus "lord, master," literally "master of the house," from domus "house, home" (from PIE root *dem- "house, household") + -nus, suffix denoting ownership or relation.
Shakespeare's usage ("Taming of the Shrew") is not the earliest in English. Meaning "give orders or directions in an arrogant, blustering manner" is from 1764. Related: Domineering; domineeringly. "Domineering suggests unfitness or lack of authority to rule, with an insulting, hectoring, or bullying manner." [Century Dictionary]