Do I need a gaming PC to play games on Steam?

You don't play the game "on steam". Steam is basically an online store and community - like the Marketplace on PSN and Xbox Live. After you purchase a game on Steam, you download the game and play it on your PC. So your PC's hardware must meet the requirements of the specific game or it won't run. Steam offers a variety of games, some of which don't have very high requirements, and some which require pretty powerful PCs. You're probably thinking of OnLive, which is a separate service. OnLive allows you to stream games. This means, you're playing the game on a remote machine and only the video and audio is being sent to your computer for display. In this setup you don't need a powerful PC...BUT you need a very fast and reliable internet connection or else you game will lag, badly, even if you're just playing single player.

That is false, if your computer does not meet requirements the only way you can play games is through online streaming (which is iffy at best). You can however get a decent PC to run most games on playable settings for 500$. You would however need to build it yourself to get that kind of a price. BTW Max, Crysis 3 is on Origin ;)

There are many types of games available on Steam. Low end games like Terraria, Killing Floor, Counter-Strike 1.6, Half Life 1, etc will run on any PC. However, high end games Crysis 3, Far Cry 3, Black Ops 2, etc. require you to have gaming PC

You don't play games "on Steam". Steam is just a download program; you run the game on your computer, through the Steam interface if the game is restrictive. This means your system needs to meet the requirements of the game itself.

It really depends on the power of the PC. Most non-gaming PCs can play Steam games pretty well, but if it's like a really low-power laptop or a fairly old PC, I wouldn't count on it.