O AIR é um aplicativo de área de trabalho, não um plug-in de navegador:
Adobe® AIR® is a multi-operating system, multi-screen runtime that allows you to leverage your web development skills to build and deploy rich Internet applications (RIAs) to the desktop and mobile devices. Desktop, television, and mobile AIR applications can be built with ActionScript 3.0 using Adobe® Flex and Adobe® Flash® (SWF based). Desktop AIR applications can also be built with HTML, JavaScript®, and Ajax (HTML based).
O suporte do navegador para SWFs mudou recentemente:
Each of the major browsers has now implemented a feature where Adobe Flash content does not run by default, but each of the browsers has implemented this feature and the user interface in slightly different ways.
Referências
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Flash Activation: Comparação de navegadores - Plugins | MDN