I imagine file privileges are akin to file permissions on *nix systems, have you tried running Steam as admin/root? (Pretty sure you can do that on windows right?), or your user permissions for the tf\ directory might have changed

I had that same problem and what I ended up having to do was just reinstall the game. But the thing is steam wouldn't completely remove everything so I had to manually delete every subfolder in tf2 manually to avoid the 'take ownership of this file' error. Could totally be the long way around but it works.

also the updates to my other games worked fine so I don't think it's a problem with the admin permissions on my steam folder

The error message says it's the file privileges.
They might not care that you don't think they are the problem.
In fact I'm pretty sure they give absolutely zero fucks about your opinion.

maybe the file is set to read only

changed the attribute of all the files in my tf folder to not be read only but it didn't fix the issue

I was talking about the steam folder since I didn't get any errors from updates to other games

Did you even read the error message?
Your problem is not the Steam folder. Neither are other games' files. That's why the update just fine.
Fucking read it.
It says "tf\resource\tf_brazilian.txt" is your problem. Of course that only affects TF2.

Dealing with broken file permissions on windows is a pointless endeavor. Delete the file named in the error message (note that it's in downloading as opposed to steamapps/common) then verify your game cache. This should force an update and re-download the file. If you can't delete the file because of its broken permissions, take ownership of it and try again.

Don't run steam as an administrator if you can avoid it. It will likely lead to other permission problems of a similar ilk.