Is McEliece secure with non-binary Goppa codes?
The problem is that you're only referring to plain information set decoding.  Indeed, for plain ISD, the complexity of attacking a Goppa code over $\mathbb F_q$ would scale as one would expect with $q$.

However, Stern's algorithm for ISD does not scale purely with the code size.

Following a geometric distribution, we can express the expected cost of an ISD algorithm as

$$
\mathbb E [\text{cost}] = \frac{\text{cost of one iteration}}{\mathbb P [\text{successful iteration}]}\text.
$$

For Stern's algorithm, given parameters $p$ with $0 \le p \le w$ (where $w$ is the weight of the error vector) and $l$ with $0 \le l \le n - k$,


The probability of a successful iteration does not depend directly on $q$ and can be expressed as a function of $n$, $k$, $w$, $l$ and $p$.
The cost for one iteration is
$$
(n - k)^2 (n + k) + ((\kappa - p + 1) + 2 N {(q - 1)}^p)l + \frac{q}{q - 1} (w - 2p + 1) 2p (1 + \frac{q - 2}{q - 1}) \frac{N^2 {(q - 1)}^{2p}}{q^l}\text,
$$
where $\kappa = k / {2}$ and $N = \binom{k / {2}}{p}$.


As you can see, the way the algorithm scales with $q$ depends a lot on the parameters $p$ and $l$.  Therefore, $p$ is usually chosen to be quite small in order to minimize the effect of going through too many subsets (the ${(q - 1)}^p$ and ${(q - 1)}^{2p}$ terms).

Please see Christiane Peters' thesis, which has an entire chapter devoted to this.  It also discusses additional improvements and proposes exact values for $p$ and $l$.

Of course, there are also Goppa codes over $\mathbb F_q$ for which such a cryptosystem would be secure.  You can find some proposals and analyses in the thesis, too.