The current release of Firefox for Android doesn't support the embedded plugins needed for Flash-based games. I think this is coming in a future version, but I'm not sure when it actually will come out of beta and be officially released.

https://wiki.mozilla.org/Mobile/Platforms/Android#Known_Issues

jscher2000 we released Firefox 14 for Android today, it has Flash support.

Many online games are designed with mouse/keyboard based actions. Unless the game developer designed the game with mobile (finger/gesture actions) in mind they generally won't work.

However only if you have Android 2 or 4 at moment I believe as Flash is not supported in Firefox on Android 3 still?

That is correct. Honeycomb support is coming very soon. Everything else 2.2+ has support for Flash now with Firefox on Google Play.