I think this is the official J implementation as it stood in 1990 when this paper was originally published, it kept being developed but not this document which describes it. Perhaps someone else knows these details?
Click on the show notes and there are links to previous episodes with him, talking about the J engine implementation, updates in J 9.03, threading and faster bignum calculations in J 9.04, updates in J 9.5, his views on tacit programming, etc.