You're comparing the version of the Linux kernel to the actual Kobo software version (AKA. Nickel).
i.e., 4.1.15 is indeed the Linux kernel (and it's unlikely to get any significant updates, certainly not anything more than a commit bump), and 4.16.13268 is indeed your FW version.
And, yeah, it's outdated, and you shouldn't have to do it manually if you're not comfortable with it, as @tayseidel just explained.
But, just in case you do have to do it manually, in a terminal, it ought to be as simple as
Code:
unzip kobo-update-4.25.15875.zip -d /run/media/$(id -un)/KOBOeReader/.kobo
It'll reboot on its own on eject.