well if you want something that can be made into SWF format to submit to this site then you will need flash which is a fairly expensive program,and from what I have seen of Game Maker when I used it,is nothing like Game Maker in any way,shape,or form besides maybe a few elements that seem to be universal to much of the game creating programs out there.I am not sure though what you are looking for exactly,as you said that you want something besides .exe but never specified,so I am only assuming this.If you want a link, then here is a link to the trial version I suppose and as for resources there are tons of resources out there for Adobe Flash,but the sad part is not much of them online actually are reliable at teaching you AS3 or AS2 in a way in which you can make any games that are decent(at least none that I have seen yet)Sorry if this didn't help you out with what your trying to do.
OH snap I fail I started rambling on so much about finding resources for flash that I forgot to post the actual link for the trial version here you go...
OK now on this page is a link to the trial version and in order to download it you must register and then sign into an account for Adobe.com which is a bit annoying,but whatever.Again sorry if this isn't what your looking for exactly.
If you want to make a game that can be uploaded to ArmorGames, it needs to be a .SWF file, which means it needs to be made in Adobe Flash. Game Maker won't work.