This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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n. The state of being knotty.

n. The quality or state of being knotty or full of knots.

n. Difficulty of solution; intricacy; complication.

n. The condition of being knotty; the state of having many knots or swellings.

n. The quality of being knotty; difficulty of solution; intricacy; complication: as, the knottiness of a problem.

n. In geometry, the minimum number of nodes in the projection of a knot on a plane or other single-sheeted, singly connected surface.

n. puzzling complexity

"Xeni visits the first-ever "Cable Untangling Championships" at Machine Project in Los Angeles, where knottiness abounds and speedy-fingered sysadmins pwn the world."

complexity    complexness   

intricacy    complication