Will
I think that's exactly what that means. If you want to play in a group of four, then it has to be Foursomes or Greensomes (everybody drives, best drive is picked for each team and then alternate shot from then on). There are still plenty of the older clubs that keep this rule: Woking, Brancaster, Rye...
(Although I suppose the wording could be interpreted as no fourball stroke play scoring? Maybe a fourball match is OK.)
Foursomes is always the fastest, even faster than singles because the partner can walk ahead and watch for the tee shot.
Keep play moving!
Ran
Broadstone is close to the Top 50 in Golf World's list. The holes above look truly world class to my eyes; I've seen a couple more photos of two different holes which look just as good.
I've asked for some more photos from the club manager which I'll post if he has them.