- If the director wasn't called, score stands. If there is no director, then either it's not important enough to care about one unfortunate board (and you should be beating them anyway if this is their calibre) or it's time to find another game where they don't do this.
- Forget transfers is my bugbear, and this time West pooched East's ability to say 4 diamonds. Maybe not 5, but yeah, still needs help.
- "2NT system on after 2♣-2♦; 2NT" is one of those things that weaker players tend to forget.
- long tank-4NT means "not blackwood, despite what it looks like". Almost always, anyway.
Luckily, this is not F-t-F, so East has the AI that partner thought it was a transfer without the UI of having announced/Alerted it. She is allowed to guess right.
As a pollee, I think you can see what my answer would be.
As director, I would not in fact trust my beliefs, because I know I'm biased (see 2., but in general) and probably not their standard (I don't tend to forget systems on after 2
♣...2NT any more). I would take the auction (without the long pause) to several players of their level and see if anybody passes. If they don't, I may ask them what a long pause before 4NT might mean (if they're the level of peer that I can expect to understand the question).
So, I probably shouldn't be polled on this one.
But I could easily see this going to 6
♦-1, or 6NT-1, or even 7
♦-2 (surely West gets it by then?) or some weighted average of the two. I highly doubt that there will be any sort of procedural penalty, and I'm quite good at giving PPs for "guessing to pass forcing bids in the face of UI" - this pair almost certainly isn't at the level where there's any chance of purposeful action, and the ruling should be "wake up" enough.
Those saying "the right system would get them there" is irrelevant; the fact that even if they do have the right system and know how to play it (which I would be surprised at) this person forgot at the table.
When I go to sea, don't fear for me, Fear For The Storm -- Birdie and the Swansong (tSCoSI)