It's actual Crusades era Muslim chainmail.
Are you sure about that? It looks like (well-made) butted four-in-one mail, and I would have expected to see
riveted mail if it was an actual working model from that period. Butted mail is far easier and quicker to make, but is not nearly as strong as riveted mail, and it requires constant repairs of parted links. That's assuming you lived to have the opportunity to repair it.
Museums are not above mixing and matching bits of armour from different provenances, and often fabricate replacement parts.
In this sample below, the riveted mail (top) would have been made from washer-like rings punched from a sheet, then joined by riveted wire links. Or, you could rivet all of them.
At the bottom is butted mail. It looks like he cut the rings off the coil with bolt cutters (which pinch, producing the double-wedged tips) instead of sawing or shearing them for a smoother-looking join.
