I've worked at several companies that use some form of go links before.
The primary advantage of them is that they are very easily self-serviceable. Anyone can create a new go link, and it's easy enough to do even the HR department managed their own.
You are definitely correct that the same thing can be handled using DNS records and something like a reverse proxy configured to route them based on the subdomain. However, that introduces permissions and ease of use issues. You typically don't want HR to have access to edit DNS records. You can relegate it to a subdomain, but at the point you're typing in "mylink.links.company.com" the shortening effect is dubious. Secondly, managing DNS records is typically technical enough that some groups like HR are not going to want to do it. And if I have to go talk to some group every time I want a go link, I'm just not going to do it.
It's shockingly useful to think "This is a page other people should know about" and be able to enter "go/page-name/edit", paste the link in the box that comes up, and have "go/page-name" go to that page on everyone's computer in the company. Done and done, you made it accessible in less time than it would take to figure out who you have to talk to get a domain name set up.
A secondary benefit is that you can enter a description in your go link. So I can just go to "go/" and get an index of all the golinks we have, with descriptions. It's sometimes useful for when I'm working on a system I haven't used before and want to see what other people have "bookmarked" about it.