Then you're in luck; based on current market trends it will soon be impossible to categorise games into genres as they'll lack any distinguishing gameplay features whatsoever. Unless "left mouse button attack" and "right mouse button attack" could be considered separate genres.
I don't think different gameplay modes are going anywhere, simply because they have different functions. However, I do rather think that we'll see a further "standardization" of gameplay modes.
I remember when every FPS had a different control scheme. It was really annoying to have to either re-map the keys or learn a different finger dance with every title. Nowadays they all have roughly the same key mappings, with perhaps just the "action", "crouch," and "jump" keys mapped a bit differently. Similarly, the control scheme for melee combat is standardizing to a left/right mouse-button system combined with directional keys for special attacks.
Similar standardization is happening with RTS titles, racing games, and simulators.
I think this is a good thing. When I start up a new game, I don't want to spend half an hour learning to control the damn thing; I want to jump in and get on with it. Having to learn a new gameplay scheme for every game is like having to manually tune your TV every time you want to watch a different program. It's a chore, not fun.
When you look at computer games in historical perspective, it's much like the development of motion pictures. In the early days, progress was all about technology and technique, with content coming second. Only once the medium had stabilized -- that is, you could just go out and buy a camera, film, and lighting gear, then send the film to a lab to be processed, then cut it and order prints -- that you could fully concentrate on the content: that's when the classics that are still remembered first emerged. How many films older than, say, 1920 can you think of? Of those, how many would you watch and appreciate beyond their historical/curiosity value? Not a great many, I would think -- yet films had been made and pretty widely distributed for over thirty years by then.
We're finally starting to reach that point, what with pretty solid off-the-shelf game engines and development kits, and these emerging standards for user interfaces, control schemes, and gameplay styles. This makes possible cross-genre games that simply weren't doable before. True cross-genre hybrids, for example. We're already seeing this in FPS's that feature vehicular combat and flight simulation.
Imagine one that adds character development, a branching storyline, well-written dialog and solidly realized characters, and solid melee combat. Then it puts you into a situation where you command a squad, shifting the perspective to a top-down RTS mode, with eventually you ending up as a general, commanding an entire army at the strategic level, shifting down to battlefield level for battles. Until recently, this sort of thing would be both unrealistically ambitious, and impossibly challenging for the player. Ambitious, because the developer would have to design, implement, and balance game engines for all these different gameplay modes; impossibly challenging because the player would have to be taught the controls from scratch every time the mode shifts.
However, if the modes are based on well-established conventions, the player would only have to practice the ones they haven't encountered before, while jumping into the game "through" the interface elsewhere -- and if they games is developed on solid, licensed, standard engines, the developer can concentrate on the meat of the game rather than the skeleton.
The golden age of computer gaming is only just dawning. The next five to ten years will see a flowering of creativity in the gaming medium that human culture hasn't seen since the 1920's and 1930's in motion pictures. Just you wait.
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A little postscript: I just noticed that there's an interesting chronological coincidence between the development of film and the development of computer games. They're just about exactly 100 years apart. The zoötrope was invented in the 1860's and popularized in the 1870's to 1880's, celluloid film was invented in the 1880's, and Edison's Kinetograph and Kinetoscope in 1893; the Hollywood studio system only really got swingin' after World War I.
OTOH the first computer game ("Space War" that ran on a PDP-11) was written in 1961, game arcades and game consoles in the 1970's and 1980's, personal computers hit the market in the early 1980's, and the Internet started to break into the mainstream in the 1990's.
So, in a way, 2007 is to computer games what 1907 was to cinema. If the chronological coincidence continues, I may be jumping the gun a bit with my prediction -- the first golden age of computer games wouldn't be due until 2020. I still don't think we'll have to wait that long, though. Unless we get a world war too...