User Zephlar found a nice solution how to start this game at Windows 10 64-bit edition. Just follow the steps beyond to enjoy Virtua Tennis 4, like I do! :)

1. Download and install Virtua Tennis 4 via steam. When you start the game for the first time, it'll install a "Games For Windows Live Redistributable"
2. De-install "Games For Windows Live Redistributable", because it seems to be an old non supported application
3. Download the newest "Games For Windows Live Client" at the official website and install: http://www.xbox.com/en-US/live/pc/DownloadClient
4. Start the client and log into your Xbox Live accout or create a new "Games For Windows Live"-account.
5. Close the application
6. Start Virtua Tennis 4. It will ask you to login your "Games For Windows Live" profile to save your progress. Do it and it will say an update is required,
7. Close Virtua Tennis 4 and accept the upgrade. It will throw you back into the game menu. Exit the game again and the update will applied.
8. Start Virtua Tennis 4 and it will say an update is reuired (again). Redo step 7 and start the game again. After sign in to your account it will take a few minutes to update your "Games For Windows Live"-account, but it works! :) I can even play online mode against other players, if there are any...

Have fun and thx to Zephlar for this nice solution! :)