I'm not a big fan of Steam, and I hate playing over my browser even more, so is there a way to download the game client from somewhere else and play it without third-party software like Steam?
After some work, you could maybe disassemble the flash loader file and download the files from the server, but you would have to keep on top of changes to the system because it seems they upgrade relatively frequently (monthly). And in all the announcements for Steam support, it lists it as a browser game, which would indicate that it has no support for other forms.
Haven't tested, but if the flash file loads files from the server in the right manner, you could potentially just download the loader file (the one the browser loads) and play it in flash player. But that is probably the best you'll be able to do for now.
With this extension you can do it: https://chrome.google.com/webstore/detail/jnppoimalombohimhmfmpldimliadlal
Open game's web page and click extension's icon on toolbar. When it fullsized game, right click and press "Save a shortcut" button. It'll download and make a shortcut to play game without browser.
Firefox version of same extension: https://addons.mozilla.org/en-US/firefox/addon/swiffout/?src=api
I believe the only place it is available is Steam, Kongregate, and the Google Chrome web store. I currently play Realm of the Mad God through Google Chrome, I find it the easiest way to play. Except that the 'Ninja' character is only available on Kongregate, until December the third, when it is released to the public.
Well adding on to X-Master of the Realm-X, you can play on Steam Kongregate, Google Chrome web store, silvergames, kabam, Sites Google, one more level, and much more. Realm of the mad god is currently going on many websites and getting very popular. I prefer Kongregate because when you get to level 20 on a ninja, you get a free Cave of a thousand treasures map that when you drop it, it opens up into a dungeon. I will say Google Chrome web store works the best but I play on Kongregate.