The original Defender's Quest I (written in AS3) runs on Linux, albeit via Adobe AIR, is it not listed as such on Steam? (If so it might be because it runs on regular flavors of Linux, but has issues installing on SteamOS due to a giant headache list I won't get it into at the moment, but suffice it to say I'm tired of Adobe AIR).
When we roll out the HD upgrade of Defender's Quest I (written in Haxe/OpenFL) we'll definitely be putting out a proper native Linux and SteamOS release.
And yeah I wouldn't mind a proper linux tester or two! For Papers Please you'd have to contact Lucas Pope and see what his plans are for that, I'm not sure if he has any.
As for OpenFL's FirefoxOS/HTML5, you should talk to Joshua Granick (@singmajesty on twitter, @jgranick on github) over at OpenFL.org about that. For regular HTML5, OpenFL uses haxe code that compiles to JS, and it has three separate rendering modes depending on the author's needs - DOM, CANVAS, or WebGL. I'm not sure to what degree it uses asm.js or emscripten.