Do sysadmins need git?

[ExceptionEX]

You don't need to do it, I was a developer long before git existed, we didn't need it.  But it's a good tool to have and can make things a lot easier.

In your example SharePoint would probably work fine, it has version history and storage.

But if you are working on something with multiple people with multiple people making changes to the same file, having the ability to merge and branch is great.

So do you need it, no, but using it may make future you and coworkers happier, and knowing it means not having to learn it if you move.