Quaternions are just the special case of a rotor in 3 dimensions, so quaternions are the geometric algebra solution.

Thankfully it's buried at the end of the article:

> Beyond 4D, you could continue using NxN rotation matrices, but since GPUs don’t support that, I’d use rotors from Geometric Algebra to simplify implementation, which is how you generalize quaternions to higher dimensions.

All hail Clifford! https://arxiv.org/abs/1401.2371 for elegant and computationally efficient methods