This sounds like an issue with the downloaded file, which can be caused by one of multiple issues:
1) Interrupted network connections: If your network connection to the download server isn't stable enough, and has hick-ups, it can cause your files to be corrupted. If the checksum is then validated against the file on the server, it is not a match, and it will retry to download the file.
2) The files on the server are corrupted: This can cause the same issue as with #1
3) The game cannot save the files at the location that it needs to. This can be caused by installing the game in the "Program Files ((x86))" directory, as that directory is normally only edit-able by administrative permissions. Most new games and launchers make sure during installation that they have sufficient permissions after the installer, by setting these permissions during installation.
4) The downloaded file is not corrupted, but cannot be extracted due to corrupted software on your system. As I'm not sure what compression method the game uses, I cannot explain how to test this.
5) Virusscanners, firewalls and electrical cables: These can also cause issues with the file, especially if the game is downloading these files through UDP instead of TCP. If you are using UTP cables instead of STP cables, then electrical cables can have a huge effect on your network connection.
6) DRM: This very much sounds like a DRM solution to prevent illegal copies of the game.
There are more possible causes then this, as the game is is not designed to run properly on Windows 8.1. You could try running the game in compatibility mode:
- Navigate to the installation directory (C:\Program Files ((x86))\Trackmania 2)
For each of the executables (Application-type files):
- Right-Click on the executable
- Click "Properties"
- Go to the tab called "Compatibility"
- Enable "Run in compatibility mode" and set it to Windows 7 or Windows XP.
In the title of this question you said you are not using Steam. What about starting to use Steam? If you bought the game, you still have the license key. As you recently tried to install it, you probably still have it nearby. Install Steam, log in, and go to the menu option "Games", followed by "Activate a product". Enter your License key, and it should activate the game for you. You can then tell Steam to download and update the game. This will save you a lot of worries.
If you chose not to use Steam because you do not have an internet connection, you can also use Steam in Offline mode. This will require you only to have an internet connection while downloading and updating the game. You will have to start the game once while connected. Then exit the game, and go to the Steam preferences. Turn on "Offline mode", and it will disconnect your Steam account from the internet. You can play games you have launched before, but will not have any of the benefits like Cloud-storage of your save games and automatic updates. If there is an update, just connect your computer to the internet, turn Steam back into online mode, update the game, and put Steam back into Offline mode.
With kind regards,