What do all of these courses have in common such that despite their obvious differences, they can all be considered "great" (whether by one man or the consensus)?
The common thread to me is all are designed to play firm and fast with wind a key design factor. Merion might be the only exception on the wind.
Royal Dornoch is the only one of these I have played, so I'll comment a little further based on my 3 rounds there over a 30 hour period a month ago.
The prior comment on the short par 4s there is spot on - they give the round flow as they are perfectly placed along with the par 5s to give the round balance. #1 is the textbook "firm handshake" with an incredible setting - my buddy felt it was his favorite 1st hole anywhere and I had a hard time arguing with that. Then 3 difficult holes, all tough pars, then the 5th as another short par 4 before 3 more difficult holes to score a par, then the 9th as essentially a half-par par 5, then the 10th, which despite being under 150 yds I never parred, tough par 4 in 11, then another strategic half-par par 5 on 12, then another solid par 3, then arguably the toughest par 4 on earth followed by another perfectly placed short par 4 before 3 difficult par 4s over 400 yards to finish.
My second observation is the variability of the test - a dream course to members that I imagine plays a million different ways based on pins and conditions.
My final observation I had was the subtle nature of the challenge. The scorecard does not overwhelm you. On nearly every hole (with the clear exception of Foxy, maybe the 18th as well), birdie is a fair expectation under reasonable winds with 2 properly struck shots. Yet, even on the easier holes, one can easily slide into double bogey range with poor decisions or execution. The old lady has horns if you cross her - but she seduces you back again after she beats you up. And the high rough, the firm and fast turf, and winds are the key tools she uses to accomplish that.
I'll leave it to others better qualified to gauge how those qualities carry over to the other courses on the list.