Not all do. Please do "About ths Mac" from your Apple menu and post what that window shows for your processor type. That will help us work this out.
The pre-2006 iMacs this forum serves do poorly with most web animation and video because web developers have abandoned support for the older PowerPC processors.
If "About" shows you have an Intel processor, it should do OK but we need to get you to the forum for those models if it's not, as something different is going on.
How are you connected to the internet, dial-up, DSL, cable modem? What is your connection rated at? What model iMac are you running? How much RAM memory do you have in you iMac? What size hard drive do you have, and how much available space do you have left on it? What browser are you using? what version of the browser are you using? How much Data Base Storage is set for your browser?
There could be a lot of factors involved in how fast the games appear to be running.