This is because you logged in as root. Basically, doing this – logging in as root, then starting the server is literally what broke it all.
This should never happen. Nobody should ever do it, but people new to Linux tend to be rewarded when they try something that doesn’t work, but doing it as the most powerful user on the system.
When you do that, you make it so only the most powerful user on the system can work, going forward (on that server).
Step 1:
Never login to the webui as root. Yes, it’s possible that I could prohibit it in code, but I don’t want to do that. If people will continue logging in as root, I’ll give them the opportunity to learn what broke, and hopefully learn to do things differently.
Step 2:
chown all your files to be owned by mc:mc (or whatever non-root user you use. That should apply to /var/games/minecraft/servers/*, etc.:
chown -R mc:mc /var/games/minecraft/servers/*
chown -R mc:mc /var/games/minecraft/archives/*
chown -R mc:mc /var/games/minecraft/backup/*
Step 3:
Never login to the webui as root. Log in as the user from the above command and try again.