OK Here goes:
Attached is a modified zip of the ajaxwhois script you posted.
Upload the folder "ajaxwhois" to /assets/snippets/
I had to modify these files to set the correct paths to images (you will not need to do this as I have done it).
AjaxWhois.php, js\mootools.js
In the zip folder you will see 3 txt files
1) in modx create a new snippet called: ajaxwhois and copy the contents of snippet-ajaxwhois.txt into it
2) in modx create a new snippet called: whoistlds and copy the contents of snippet-whoistlds.txt into it
3) Create a new page in modx set the template to be used to none, hide it in the menu, turn of cachable and call it something like whois
then enter this into the page content
[!ajaxwhois!]
Once you save this make a note of the page ID (the ajax search calls this page in the background to get the results)
4) Create a new page for the domain search form
Paste in the contents of searchpage.txt
now you will need to modify one line in here to point the form to the whois page which you created above
look for:
<form id="whois" action="[~73~]" method="post" >
change the 73 to the ID you captured above and save the page
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It should now work in MODx for you.
Aaron