I researched the matter and I was surprised by what I found. There seems to be a bit of a quaternion mania going on. Quaternions are documented extensively in books, articles, and on the internet. Programmers are using them to write games. It seems to me, they are not.
Quaternions are a mathematical oddity.
They involve imaginary numbers and a 4th dimension. They have a unique algebra, with the multiplication operations being particularly unwieldy. They do the job they are asked to do. I don't think so. Here is a common matrix representation of quaternion rotation.