The genre of Coriolanus is often debated due to the fact that it is based on the life of a Roman general who, during Shakespeare's time, was taken seriously as a historical figure like Julius Caesar. More recent historical scholarship has argued that Coriolanus existed as a legendary figure in Roman history rather than an actual person, but in early modern England most would have agreed that Coriolanus and his martial victories actually existed.
Why, then, is Coriolanus presented as a tragedy in Shakespeare's work rather than a history? The answer is multifaceted and mostly speculative, but it is worth noting that many of Shakespeare's other "Roman" plays (as they are colloquially known) are also demarcated as tragedies rather than histories. The most notable of these historical tragedies includes Julius Caesar and Antony and Cleopatra, the latter of which Shakespeare wrote at around the same time as Coriolanus.
In fact, Shakespeare's history plays are almost exclusively devoted to chronicles of English history rather than narratives of other empires. When a play appears specifically as a "history" in Shakespeare's folios, it more often than not delineates the narrative surrounding English kings like Richard III, Henry IV, Henry V, etc. It would seem, then, that despite the historicity of Coriolanus and the plethora of source material available on the subject (Livy and Plutarch, namely), Shakespeare saw Roman history as separate from English history, and thus included Coriolanus among his tragedies. Furthermore, Coriolanus details the rise and fall of one ambitious man, a plot common for tragedies and for Shakespeare's tragedies in particular.
