There was Psion Chess for the expanded ZX81 (16 KB RAM.) I still have the cassette. The instructions on the cover explain how to castle and state that it recognize en passant. No mention about promotions but they should be supported.

Load time "3.5 mins approx." I remember that I lost every signore game against it but it wasn't very fun because it used fast mode and I couldn't see the screen when it was thinking.