What is the purpose of verb reduplication? In English, we can say:

I sneezed a big sneeze.
She sleeps a long sleep.
"Waiting for a king to apologize, one can wait rather a long wait." (from the film The Kings Speech)

and many more such examples.

Just one chapter of  西游记 has these five reduplications with  了 between.

Do you think the word after 了 is a noun or a verb? What is the purpose of the reduplication?

猪八戒抬手指了指天，
孙悟空看了看猪八戒的大肚子，无奈地笑了笑说，
拿着金箍棒晃了晃，对准马屁股作势要打。
，强盗头目眼珠子转了转，
一边说还一边向着猪八戒挥了挥手里的金箍棒。  

For comparison， 了 followed by a noun:

你要真的抢了我的东西，
，如果这辈子做了坏事
强盗头目得到了满意的答案，
The examples you gave are not verb reduplication
phrases like 笑笑，看看，走走 or 吃吃 are verb reduplication, it serves to indicate the verb is in a slight degree or a casual manner

I sneezed a big sneeze
She sleeps a long sleep

These are just a same word as verb, and then as noun (object) in a same sentence

the first sneeze is a verb; the second sneeze is a noun

the first sleep is a verb; the second sleep is a noun


了 is not a verb, it is a 'verb particle' that indicate 'completion of the action' or 'change of situation.
In your 西游记 examples

指 = point

指了= pointed (the pointing action is completed)

笑了笑 - the first 笑 is a verb; the second 笑 is a 'verb classifier' for counting how many times the subject smiled (since there is only one smile, the action is in a slight degree or casual manner)

晃了晃 - the first 晃 is a verb; the second 晃 is a 'verb classifier' for counting how many times 金箍棒 was swung (since there is only one swing, the action is in a slight degree or casual manner)

转了转 - the first 转 is a verb; the second 转 is a 'verb classifier' for counting how many times 眼珠子 was turned (since there is only one turn, the action is in a slight degree or casual manner)


Since the second 笑, 晃 and 转 are verb classifiers, they work with counting words: 笑了(一)笑, 晃了(三)晃, 转了(八)转

抢了我的东西 (seized my stuffs) - '抢了' is a completed action; 我的东西 is the object
抢我的东西 - (seize my stuffs) - '抢' is a verb; 我的东西 is the object (no indication of either the action is completed or not)

~

'做了坏事' (have done bad thing) - '做了' is a completed action; '坏事' is the object
'做坏事' (do bad thing) - '做' is a verb ; '坏事' is the object (no indication of either the action is completed or not)

~

'得到了满意的答案' (have got a satisfied answer) - 得到了 is a completed action; 满意的答案 is the object
'得到满意的答案' (get a satisfied answer) - 得到 is verb; 满意的答案 is the object (no indication of either the action is completed or not)