Gospel of Luke Genre
It's All In the Preface
Luke makes it pretty easy for us. Right in the preface (1:1-4), he prompts readers to expect that a history will follow. And sure enough, Luke and its second volume Acts are together widely considered a work of Greco-Roman historiography (or history-writing).
Other ancient historians wrote similar, but usually longer, prefaces, which are dedicated to various figures just like Luke dedicates his work to Theophilus. Luke also mention a few important standards for successful history-writing: reliance on eye-witnesses and other early sources, thorough research, accuracy, order, and "truth" (1:4 NRSV) or "certainty" (KJV). Luke even uses the key term "narrative" (1:1) to describe his account (the NRSV and the KJV translate the Greek word here somewhat misleadingly as "account" and "declaration," respectively). This term was used in ancient literary criticism to describe narrative-genres, one of which was—you guessed it—history.
Checking off another box, a lot of Luke's content overlaps with ancient histories, which include accounts of dinners, lengthy speeches, genealogies, and super dramatic events.
But before we get ahead of ourselves, we have to remember that Luke-Acts being an example of ancient history-writing does not mean that Luke-Acts is an accurate representation of history itself. There are in fact some downright errors, and there's definitely an effort to shape the story of events so that it communicates specific meanings and conveys theological insights.
So we can say that Luke's history is history with an agenda. And hey, that's actually in keeping with the nature of ancient history-writing in general. Some thinkers go so far as to argue that all history-writing is history with an agenda, even when objectivity is emphasized—then and now. But we'll let you duke that one out with your friends.