I don't think an area can count as shelter if it is not also walkable (blue) area. My experience with walkable area is also that it only appears on higher climb-to-able surfaces if there is also a way to walk onto that area, rather than just climb to it (then it counts as climbing). A climbable floor piece would still be able to be walkable and count as shelter in the same situations a non-climbable surface would qualify for those features, so you should be able to use either, it's just quite complicated to get the game to qualify an area as walkable. Whenever I want some piece to count as walkable I always have to create a ramp up to it from another walkable area, which is not always visually what I want, but it gets around it. You could also try to make a very small piece of terrain just above the floor of, or next to, your structure, to create a kind of "getting off" point of the climbing frame, which they can then walk onto your floor area from.
I think a secondary thing is that if a roof is too high it stops counting as shelter? Perhaps the roof would need to be a little closer to the floor pieces, but I think getting the floor pieces to show up with blue walkable area is the primary thing you need here.