So I joined in part to respond to the answer about comedy, tragedy, and romance. Short answer: the “romance” genre in plays has a big messaging problem.
The best alternate term for a “romance” play is adventure, not love story. I don’t fault Brandon or Lucy going to “love story,” given what romance means in present-day terms. However, Shakespeare’s late plays (Pericles, Cymbeline, The Winter’s Tale, The Tempest, The Two Noble Kinsmen) were called romances because they resembled medieval romances, or adventure stories with a lot of travel (including rudderless ships and shipwrecks), individual struggles (getting back a throne, growing up, trying to find your family), occasions for humor, magic, knights, and other elements. The medieval romances were a huge influence on what became the “hero’s journey” and the modern fantasy/sci-fi template.
The closest comparison between a romance play and games is arguably the JRPG, which features a lot of travel (including rudderless ships and airshipwrecks), individual struggles (getting back a throne, growing up, trying to find your family), occasions for humor, magic, knights, and other elements. A Roberta Williams game would also be a good fit, as would, well, many big blockbuster games. I’d almost argue that whereas you’d have to stretch comedy or tragedy to fit video games, many video games fit the old romance model.
I liked the rest of the answer, especially Stanley Parable as an example of comedy and Yoko Taro games as tragedies.