Flash is still a great platform for developing games while HTML5 catches up in terms of a consistent cross platform experience. However I find the open source development tools to be much more convenient. For e.g. FlashDevelop is an excellent IDE if don't require the animation tools. Haxe is a great strictly typed language that has a fast compiler targeting Flash.
The most promising project for games is Cocos2D Javascript bindings: same source code runs on HTML5/mobile/desktop taking advantage of native GPU accelerations. Cocos2D is the most popular 2D engine for iOS and was ported to other platforms as well.
This is confusing. Did Adobe change their mind after completely giving up on mobile last year? What changed? Everyone I know who's done mobile development with Flash/AIR hated it - have they improved the tools? Or is this just piggybacking on the fact that tools like Unity target Flash's runtime for desktops now?
I also remember seeing news articles about Adobe refocusing on HTML5 and putting out HTML5 development tools to replace Flash. Did they give up on that or is it still in progress?
AIR is still a convenient way to create cross-platform desktop apps as well. I've been trying various HTML platforms I can find and haven't found an alternative that I think works as well. It's a shame that the developer community has shrunk so much. It's rare to find people doing or posting about new things.
They never completely gave up on mobile, they gave up on mobile in-browser plugins, essentially because they realized they'd never be let onto Safari.
They've continued to develop Flash/AIR tools for standalone mobile apps and the tools have improved quite a bit though obviously they still take a speed/size hit compared to true native and the resulting apps feel not-quite-native on any of the supported platforms.
They are still highly focused on HTML5 for their traditional non-game users (mostly people in marketing and advertisement and other interactive design fields). But they're also focused on keeping the Flash platform going as both a cross-platform mobile app solution and a "game console for the web".
Their strategy here hasn't really changed since Adobe Max 2011 but their message has been twisted a lot by various "camps" both pro and anti Flash.