Can you check once again at that website? I couldn't find any such links which show me that they are hiding affiliate link. They are only using clocked link.
And, it simply redirects to the Amazon link.
I guess you want like this.
You want to show your visitor non-affiliate link
but you want them to redirect to the affiliate link after click
Damn! What a clever idea!!
I don't know which plugin can do this. But here is the simplest way to do this
For more, see here.