No, not the config files. This section came after the scenario when you only want to share your games between different distributions.
What I was saying about the home directory and different distributions was that when you just couple your single home directory to all distributions then all config files are shared too.
That’s the first question you need to answer for yourself:
Is your goal to just share the games / lutris data / steam data?
Do you need to share the complete home directory?
If the second is the case, then you need to know that different distributions use different versions of programs. What happens when a program version 1.0 saves a config file to
~/.config/program/config.json and in another distribution the same program but then version 1.2 does the same and this program uses different settings which version 1.0 doesn’t know about?
Another thing to keep in mind is permissions. On every system a user gets a unique ID. Who will own the home directory? The stackoverflow post addresses this issue too.
TL;DR: its much easier to let every distribution have its own home directory and pick the items you want to share. You keep the systems as they were designed for and you have control over the shared parts.