Gaming will stay on desktops for some time, until at least it's effective from a pricing point to go mobile.
Here in the UK at least I can't remember the last office I went into where desktops weren't dominant.
Also, I have been to a steadily increasing number of offices in recent years where everyone had laptops (typically Dell, I think) with docking stations and monitors. This is usually to make it easier for presentations, attending conferences/training days and working from home.
They are mostly utter garbage, more in the Zynga 'social' angle than anything else. The majority of what's left have incredibly simple gameplay mechanics, because the control schemes open to you just don't allow any more complexity. apart from the gyroscope, which I'm not convinced anyone will ever use well, all your input methods involve you obscuring the screen with your fingers!? And can never provide feedback to the user!? Madness.
Mobile gaming is huge, and it makes money, but mobile gaming is a bit like 'social' gaming: it is not actually 'gaming', as gaming is on other platforms. These things exist side by side, one does not replace the other.
On the social gaming side, I agree that very little of what you do in things like FarmVille actually seems like gaming, but then that was also my experience with much of World of Warcraft…
I think you just have to give it time -- gaming on mobile devices will probably grow up with the users, who seem to be predominately younger folk and teenagers from what I've seen (referring to mobile gamers here, not smartphone users in general).
Also, I have high hopes for the low initial cost and easy in-app purchases finally leading to some decent story-driven episodic games.
Imo, mobile gaming is good at: - The tiny subset of games where the controls are naturally dragging your finger over glass (Fruit Ninja, those airplane landing games, not much else) - Turn-based games where the primary form of interaction is suited to a one-click mouse / finger. Turn-based because there is not enough feedback for accuracy in real-time games, and because it means you pick them up and put them down really easily (as long as state is remembered) which suits on the go play.
So stuff like Civilisation, turn-based 4x games, final fantasy style RPGs and XCOM style games are all good deep game genres that will hopefully make a competent jump to mobile.
I see that Frozen Synapse (XCOM style-ish) is coming to iOS, which is particularly awesome (more awesome if it was on tablet android, but that's just my selfishness talking)
In addition to those you list, I would say that anything largely mouse controlled on PC should work reasonably well on mobile devices -- RTS games, Diablo-type games (looking forward to infinity blade dungeons) and sim games (theme hospital, etc.).
In fact, the only games I'm really missing on iOS are the FPS games. And it really is just the attempt to have virtual dual-stick controls that I dislike -- the games are there (mass effect infiltrator, dead space, etc.). If someone could just produce a decent Bluetooth controller and get developers to support it, I'd say that iOS could be the most well rounded gaming system out there -- capable of both console-style gameplay as well as game types that are weak on consoles (RTSs and the others listed above).
I'm also excited about onlive, which I already use with the TV-connected box. I think they were also working on a universal controller…