Term for non-ARX symmetric-key cryptographic primitive design strategy What's the term for describing designing symmetric-key cryptography primitive out of bitwise operations and shifts and rotations? 

The closest thing I've found is this Keccek team's page calling it NORX, but the linked reference says NORX is actually an AEAD algorithm.
Primitives based purely on bitwise and shift/rotate operations can be described as being based on:

Binary Polynomials

Bitwise and, or, not, xor are element-wise $\mathbb{F}_2$ additions and subtractions; $n$-bit shift are based on multiplication by $x^n$ reducing $x^w$ where $w$ is the width of the word; rotation are based on multiplication reducing $x^w+1$.