Hi.
In this guide, I'll show you how to fix blurred textures with Non-Steam installation.
I'm using newer graphics card GTX1050Ti (4GB). And it's weird to see low-resolution textures on a newer graphics card. So I tried to find how to fix this. The only way was to play it as a Non-Steam game. But then I've got an idea to copy that into the original Steam game, and I'll show you, how I did it.

You'll need a Non-Steam game to fix this problem. I've found a direct link with the Non-Steam version.
(This link will open you download tab with game.)
http://files.trackmaniaforever.com/tmunitedforever_setup.exe

After that, do the installation of the Non-Steam version. Because we need only files inside the game, it will be in your pc temporarily. So I recommend disabling the start menu folder.
(Don't download it to your steam file as I did, download it anywhere else.)
At the end of installation make sure, that you'll not launch the game.
(It's a waste of time.)

After installation go to the non-steam version folder.

Double click to open the folder.
You'll see some files.
Select all files and hit copy.

After that, locate the original Steam game that you want to fix.
Hit replace files.

Here you can see which files have been replaced.

And that's all.
I hope that worked for you. If not, try other ways.

At the end of all, I'll show you before and after.
Before
After