There are many types of games, RPG game, MMORPG game, multiplayer game, browser game, adventure game, mission game, mini game and etc. Today, I will focus on mini browser game, specifically HTML5 browser game. Why HTML5? Because HTML5 is used on all browsers and all devices. No matter what devices you use, be it iPhone, android phones, windows phones, or any browser you use, be it Chrome, Mozilla, or Opera, all runs HTML5. As a game developer, my company focuses on making HTML5 game, and there are several game engines available to make your own HTML5 game.
If you were to visit a forum dedicated to HTML5 game development, html5gamedevs.com, you can see some forums dedicated to the game engine. I am currently learning how to use Phaser game engine. My company uses ImpactJS game engine, which is not open source, and can be bought for $99. For a list of HTML5 game engines, you can visit here.