If you've nothing to keep in the original GTR2 install, personally I would just uninstall from Steam and start again. Re-install GTR2 fresh from Steam, unpack the Anniversary download, copy all the files to your GTR2 folder (overwriting any files when Windows prompts), and you're all set.
If you want to keep the original Steam version and run two separate GTR2 installs (as I do), then temporarily rename the GTR2 root folder in steamapps/common, then install GTR2 again through Steam, rename the root folder again of that new install (I just use "Modified" on the end of the folder name), return the first install folder to the original name, and you're good. Steam will know no different, and you will have 2 separate installs: 1 for 10th Patch, 1 for "Vanilla". To get the 10th Patch version to show in Steam, you need to use the "Add a game" function in Steam, point to the 10th Patch GTR2.exe, add a nice custom background and logo in Steam, and go race like it's 2006
If you want to keep the original Steam version and run two separate GTR2 installs (as I do), then temporarily rename the GTR2 root folder in steamapps/common, then install GTR2 again through Steam, rename the root folder again of that new install (I just use "Modified" on the end of the folder name), return the first install folder to the original name, and you're good. Steam will know no different, and you will have 2 separate installs: 1 for 10th Patch, 1 for "Vanilla". To get the 10th Patch version to show in Steam, you need to use the "Add a game" function in Steam, point to the 10th Patch GTR2.exe, add a nice custom background and logo in Steam, and go race like it's 2006