“Piñatex is a byproduct of the food industry,” explained Hijosa. “Once the pineapples are harvested the plants are left to rot.” Instead of letting that happen, pineapple farmers gather the leaves, extract the fibres and degum them in closed tanks. Once they have been degummed, the fibres become soft and breathable and can be put through a mechanical process that turns them into a non-woven mesh material that ends up feeling much like felt.
from here
It looks like the pineapple leaves are treated with a process something like
flax or sizal to extract the bast fibers.
For flax, the plants are retted (controlled rot) to remove some of the 'glue' that holds the fibres to the rest of the leaf. Once dry, it becomes relatively easy to separate the fibre from the stem. At this stage, if processing by hand, we have a long fibre that is excellent for spinning and shorter fibre which makes an inferior yarn. This short fibre is called tow and can also be used to make a kind of paper. Lay the tow in layers, with the fibres facing different directions (first layer horizontal, second verticle, and so on) until it is 5 or 6 layers thick. Place them between two window screens, and thoroughly wet the fibre. Use a rolling pin to apply pressure, rolling back and forth, and the natural pectins and other elements in the fibre will glue the tow together to create a kind of paper.
Going from the description above, it looks like a variation on this method, only perhaps with some other binding agent? It looks like it is dried on a textured surface to create the leathery look. I don't know how it is made waterproof, that's why I'm guessing another binding agent.