Of all the cheetahs alive today, many have the same or similar genetic qualities. 

of后面的结构是类似于with+独立主格结构吗？

解答如下：

你的理解有误，属于“形容词alive作后置定语”修饰前面的名词cheetahs(alive属于表语形容词，如果作定语必须后置）

A:作后置定语用法

He was the only one alive then.  

他是当时唯一活下来的人。

Thousands of Chinese miners, dead or alive , were thrown into the death pit by the Japanese fascists.  

数千名中国矿工,不管死的活的,统统被日本法西斯扔进万人坑里去了。

Who is the greatest man alive?  

谁是目前世界上最伟大的人物?

B:作表语用法

The old man is still alive.   
那老人还活着。

Are your grandparents still alive?
你的祖父母还在世吗？

Many great writers were not appreciated fully while they were alive.  许多伟大的作家在世的时候并没有得到人们充分的赏识。

He accounted himself lucky to be alive.   
他认为自己能活着就是幸运。

You shall never want for money while I am alive.   
只要我活着,你不会缺钱花。

The elephant was still breathing, so we knew it was still alive.   
那头大象仍在呼吸,所以我们知道它仍然活着。