‘Modern’ in social/historical use can refer (roughly) both to periods of time, works and ideas from those periods of times, and to characteristics perceived as modern. There’s a rough consensus about the period we’d call modern history, and a different one in philosophy/culture/art theory about the time period encompassed by the movement called Modernity.
Handily, the word ‘modern’ has become shorthand for new or up-to-date, reflecting trends of today, or occasionally, forward-thinking. So in common use, the adjective ‘modern’ has already uprooted itself from the tradition of being used to describe work from a particular period of time. People will keep on using it to describe the work of today. Though obviously it’s still used in its original sense when the context suits.
Post-modernity is more fluid and less time-anchored than the modern or Modernity. It’s basically an agreement (or discussion. or ongoing argument) about shared characteristics of works and ideas in an environment more complex than the modern. It doesn’t say: ‘Post-modernity began here, in year X, and all the works from then on are postmodern.’ If something made 150 years ago happens to match various criteria for postmodernity, it’s still seen as game to mount an argument for that thing being postmodern. Or at least to indicate that it expresses characteristics we now identify as being postmodern.
Most mainstream entertainment has become casually postmodern. Self-referential, referencing each other, fourth-wall-breaking, more ironic than earnest, hyper this and hyper that. (Jean-Baudrillard was big on the ‘hyper’ prefix. e.g. hyperirony) The Simpsons is probably the fundament for everybody being able to understand postmodern characteristics while rarely ever hearing them called postmodern characteristics.
So, having recounted my uni day memories of modernism and postmodernism, my opinion on the topic is probably equally tangled. IF is definitely characterised by a ton of postmodernity now, and probably has been since its start back in what’s been called ‘old IF’. It’s been the nature of people who made things on computers in the mainframe and microcomputer years that they exercised postmodern tendencies ahead of the curve. The concept of the modern here is relative to IF’s short history, and represents an expansion of subject matters and techniques. So IF was postmodern, for cultural theory purposes, before it became modern! For that reason, and due to the nature of the project of postmodernity, I don’t think you’d ever want to define a period of IF as postmodern. Even though a lot of IF is now extremely postmodern.
Maybe the next main trend in parser IF was player-friendliness, and it continues. Maybe there’s some word to reflect that that doesn’t sound awful.