The most recent Steam beta update allows you to use your custom controller configs on any PC with Steam installed.
Valve has deployed a new beta client update for Steam that’s changing the way it handles Steam Controller configurations. The new update makes it easier for the developer to deploy configuration-related features and updates.
Basically, it lets you take your controller to any other PC running Steam, and continue using your configurations there, even if you’re not logged into your account. The same can be said for games that support multiple controllers, this allows each one to have its own configuration.
Another positive side effect of this change is making things easier for sharing community configurations for non-Steam games, according to Valve.
After updating your client, Steam will ask you to “register” your controller with your account, which is Steam’s way of knowing which account to grab controller configuration from. This needs to be done for all of your current configurations, but it’s a one-time process.