Dividing elements in $R_q$ by $z$ in Grag-Gentry-Halevi (GGH) Graded Encoding Scheme
I believe $R_q$ is not field


Yes, it is not a field in general. $R_q$ is a field if, and only if, $q$ is a prime and $X^n+1$ is irreducible over $\mathbb{Z}_q[X]$.

However, you are not forced to pick $q$ as a power of two. As section 4.2 of the original paper explains, the only restriction over $q$ is

$$q \ge 2^{8\kappa \lambda}n^{o(\kappa)}$$

In particular, you can let $q$ to be prime (as it is supposed to be in Lemma 5).

And even if you don't select $q$ as a prime, you just have to check that $z$ has an inverse in $R_q$ and that the order of $z^{-1}$ is bigger than $\kappa$. If this is the case, then you are fine, if not, then sample another $z$.