I think the "you need x,y,z players" to win a cup is an exhausting conversation because more than half the time, you need to go back and retroactively apply a label to a player.
For example, no one on the planet would have tagged Eichel as a true cup caliber #1C before he won - He was coming off of his third straight sub PPG injury riddled season.
The best teams are usually the ones with the fewest holes (that was not Colorado this year and its a point I tried to make several times while they were being glazed by everyone, Lindgren was their #4 and he is legit a guy you cannot win with in your lineup) and players who are capable of playing to a certain level - It's not about a label because it's not always the best guys who come through (see: #10)
Sometimes those guys are elite (MacK, Crosby, Point, M.Tkachuk, etc) and sometimes they aren't (Marchessault, ROR, Verhaeghe, etc.)
The NYR's issue is that they have suffered from pretty much all of the above.
Just using last year as an example - Too many holes (Lindgren and Trouba in their top 4, a 3rd line that accounted for 3 goals for the entirety of the playoffs.)
Not enough people capable of really stepping up and playing at an elite level - If we're using last year as an example, They got more than they expected out of Trocheck, Igor, Lafreniere and some how, a 6 goal run from Goodrow (I will forever be annoyed that they booted Goodrow's output because you just aren't getting that from a 4th liner again.)
The only guy who really performed at an elite level of that group was Igor (whose play in the post season is honestly underrated here. He's levels better in the playoffs than even Hank was.) Trocheck (bordered on "elite" performance) and Laf gave you very strong supplementary production/performance, but everyone else did either bare minimum to carry their weight or were underwhelming, bad or catastrophically bad. Goodrow honestly sucked, but 6 goals is f***ing 6 goals. Thats more than the Rangers got from everyone other than Kreider, Trocheck and Laf.
It would have also helped if our actual "elite" player actually played like one.
tl;dr: "elite" or "generational" labels don't really matter. You need to have quality depth and players capable of stepping up. Rangers haven't had enough of either and it's been both masked by how good #30 has been in the playoffs and magnified by #10 basically turning into a run of the mill secondary scorer in the playoffs.