There seem to be differing views of what “genre” is, at least as it pertains to video games. I suspect partly this is due to the fact that there are differing views of what a “game” is. One viewpoint, which is probably working its way forward as we speak: “Why does it even matter?” The answer is very simple, and gets back to the entire point of language in the first place.
We use tokens (sounds, letters, images, etc.) to communicate. You cannot communicate effectively without an agreement on the meaning of the tokens. If you think that “cheese sandwich” refers to a piece of cheese between two slices of bread, but I think “cheese sandwich” means being stuck between two tv news anchors, our conversation could get rather confusing.
Of course, conversations can (and do) get confusing all the time, because lots of words have multiple meanings, nuances, and associations, so in order to have a formal* discussion on a particular topic there must first be a clear agreement of the meaning of particular terms used. This is why any field develops its own jargon, and why academic articles, textbooks, contracts, etc. can come across as characterless and bland.
Some may still be asking the same question. After all, they’re only games; why would we want to be formal about them? Thus we turn a corner and bump into the “Can games be art?” debate. For what it’s worth, I think they can be, but that’s not really germane to this topic (genre, in case you’d forgotten. I almost had). Regardless of their artistic merit, games are certainly worthy of critical** analysis. If we cannot examine what worked (or didn’t) about a particular game, how can we expect to make the next game better? Plenty of movies have the aim of entertainment, without aspiring to high art, but still benefit from a clear understanding of the art of cinematography.
So, back to the topic: How to define genres for video games? To a large extent, I suspect (as implied by the title), that genres emerge from the exploration of a medium as the creators codify aspects that work well together. They can be influenced (basically, given a head start) by pre-existing genres in another medium, but they must take into account the techniques and details of the newer medium. “Hard-boiled” detective/thriller novels served as inspiration, but noir is a uniquely filmic genre (including particular styles of plot, lighting, music, etc.).
Similarly games must establish their own genres based on the features of the medium. Aspects of look, tone, plot, etc. can be taken from other media (film seems a particularly favourite source of inspiration), but the “ludic” aspects must be involved as well. We can see the beginnings of this: a FPS (First-Person Shooter) would once have been referred to as a “Doom-clone”***. However, I think these “genres” are as-yet too broad to be of much use; the genre of a game should give an indication of the style or tone as well as how you interact with it. For example, Doom (horror/action) and Portal (sci-fi/puzzle) could both be classed as FPS.
I’m confident we will eventually settle upon a more useful classification system; we just need to keep paying attention to what aspects of a game contribute to the overall experience.
* As opposed to a casual conversation. Most of the time, people are content to accept a little ambiguity (which is often quickly resolved by context) in order to facilitate conversation.
** That’s “critical” as in “critique”, not necessarily “critical” as in “criticism”.
*** A particularly notable example is often the starting point for establishing a category, which will probably be called “things like X” until a more suitable name is decided upon. An example of the transition can be seen in the debates over the term “rogue-like”.