So it seems like the 1.02 update for Pinball Arcade unlocks all the tables for free. Normally you can just download the base client for free, but now all the additional tables are also listed as "purchased" now. There's no need to download anything separately beyond just the base game.
I've only tested this on the PS4 version.
This is probably just a glitch and won't last very long so enjoy the tables while you can.
Edit: And now some people on Reddit are reporting it's no longer working so YMMV.