I've read this article a while ago (I think it's about 7 years old), and with all respect to Shreeraj Shah (the author) I completely disagree, and I extend my disagreement to most of his "security" methodology. Security by obscurity isn't the answer!
Here's something taken from the original (IN)SECURE article (page 25) explaining the benefit of this technique
This fingerprinting technique helps in determining the type of client
code that has sent this request. It is possible to lockdown resources
for just the right client on the server-side as well. This type of
header is harder to add by automated crawlers and bots since the logic
and calls need to be understood first. Consequently, automated attacks
on your Ajax resources can be avoided.
Mr. Shah is assuming that his method adds security because he's leveraging the attacker's ignorance of his request method.
My personal opinion is to treat this as false information, or outdated information at best.
Now that I think about it a bit more, I think I haven't targeted your exact question
Are there any Benefits of Ajax Fingerprinting?
I don't see any security benefits for that at all. There might be some benefits regarding the usage of the application. One example would be a URL like this
You might wanna view the article when the page is visited normally and provide the information in JSON or XML if the same URL was requested with Ajax.