Wow so many people using different engines! Luxe is very interesting - I haven't looked into it... but I have developed in Haxe and OpenFL.
Construct 2 and Game Maker are super awesome. I don't have much experience with these either. GameMaker I must say, super impressed with some of the games developed in it - Hyper Light Drifter... omg.
I develop mainly in Flash (now renamed to Adobe Animate). I've been making Flash Games since 2005, and have my first title on Steam this year -
Armed with Wings Rearmed.
Rearmed is developed in Flash Pro 2015 targeting AIR Desktop. Flash is great to develop desktop games in, super quick, flexible and can be quite powerful .
I've also worked in Unity, pretty standard stuff. I much prefer developing in Flash over Unity, I just wish Adobe supported as many targets as Unity does.