Why is a new GameMode Object created for each local Player?

Hello FelixSab1, thank you for posting and welcome to the Unreal Community.

Your concern is quite interesting.

I am not seeing anything that explictly spawns your GameMode (again) so I would check for any references with reference viewer. This may help you find if anyone else is trying to spawn it in.
I was unsure about the documentation you were referencing, would you be so kind as to share that link if possible.

Another note: Reviewing this video might help you with troubleshooting your player spawning method.

WARNING: This is an external link and as the end user, you are responsible should something happen to your device when you choose to click a link or follow steps that are not endorsed by Epic.

Red Line Games (YouTube Video)

Since you are making an RTS, I would consider using ints rather than tags, if possible. You may need ints for when you implement your turn-taking mechanic.

I hope this helps you along the way.