If I don’t require user interaction I would use a toast?
You can still use Snackbar. It is not mandatory to have an action with Snackbar.
What is meant by “system messaging”? Does that apply to displaying
information when something important happened between my app and the
Android system?
I believe this means that Toasts are to be used if there are some messages pertaining to the system. Either android as a whole or some background service you may be running. E.g. Text-To-Speech is not installed. OR No Email client found.
What I like is the swipe off screen feature – would that be a reason
to start replacing toasts with Snackbar? (this is a bit opinion based
question though)
That is one reason. But there are several other plus points. For an example: Your toast remains on screen even when the activity is finished. Snackbar doesn’t. There is less confusion if the toast does not popup (or keep popping up in case of multiple Toast creation in sequence) long after the app is exited. This will not happen with Snackbar.
More than everything: I suggest if you are thinking, you should switch. SnackBars look far better than Toasts.