My personal policy is to never register any product for a guarantee for the simple reason that I don't want my name distributed to every merchandising outfit in the whole world. I get enough junk mail (and pop-up ads) as it is.
At least your linked registration form doesn't ask the usual nosy demographic questions about income and education levels, marital status, recreational preferences, whether you own a dog, and whether you're circumcised or not.
Besides of which, they must already have firm records of your purchase anyhow.
I believe that at least the original manufacturer must honor their guarantee, "registered" or not.
This personal policy has nothing to do with not letting the aforesaid "whole world" know I own a gun.
Terry