I do think that some of the perceived effects are skewed, in that a lot of casuals that play games on iOS devices already did so as browser/flash games. Now it gets the (significant) enhancement of being playable on the move, but I currently think games played on stuff like the iPad take over primarily from on the one hand tabletop games and browser/flash on the other, and not nearly as much as people think from handheld game devices. At least so far - it surely has the potential to do so still of course, but above all I think hat we'll just see more of these devices overall, not a shift per se.
Funny you mention this because I'm pretty sure the opposite is equally true ie there are millions of people who game on iOS devices that have never played any type of flash games on computers or other devices. In fact I myself wasn't even aware that some of the iOS games were ports of flash games for computers until I visited the developer/publisher sites.
As a hardcore gamer and someone whos owned, Pong, Atari 2600, Vectrex, NES, SMS, SNES, Genesis, TG16, ,TurboDuo, SGFX, PS1, DC, GC, PSTwo, X360, GB, TurboExpress, DS, PSP, GBA I can honestly say there are valid reasons why iOS games are so popular. No need for excuses.
1. Easy to buy from App store, most games can be purchased and downloaded immediately wirelessly straight into the phone in only a few minutes no matter where you are as long as you have a cellular signal.
2. Games are small in size and are not physical so you can have over 100 games on the device without having to carry around "cartridges".
3. Games are cheap and some are free with ingame ads. Some non free games can be had for free via Free App A Day type sponsors. Just because they're free or cheap doesn't mean they aren't fun. If they aren't fun people wouldn't be playing them they'd be moving on to something that is fun.
4. Games are easy to pick up and play and don't take tons of time to get familiar with complex controls.
5. Many games are made to be playable using only touch and motion so you don't need dedicated bulky controls on the device.
6. Games are simple yet addictive because they have classic gameplay mechanics and most support HD resolution so they also look great. Sound quality is great too when using headphones. A lot of people overlook this.
7. Online multiplayer, leaderboards, achievements, social networking etc.
8. No need to carry around an extra device just to play games. Also since these games don't require lots of time to play they don't drain the battery so much, so if you're gaming on your iPhone there is little concern when you want to make a phone call.
Of course there are drawbacks too but they're irrelevent for the type of gaming that people do on these devices. For example no dedicated controls for traditional non touch games. This to me is irrelevent because it adds complexity, bulk and just doesn't make sense on a device so small. I leave those complex games to my home console. Before iOS people didn't have a choice, if they wanted to play games on the go they had to choose between Nintendo or Sony dedicated portables. Now that there is a third choice the other two becomes less of a requirement.