Question: Does AIC require the residuals of the models to be compared to be normally distributed?

Answer: 
To answer your question, see below that we are using the letter $f$ twice. That's because this framework assumes you're looking at the right class of models. 

(Twice) the Kullback-Leibler divergence between your model's density $f(\mathbf{x} ; \psi)$ and the true model $f(\mathbf{x} ; \theta)$ is

\begin{align\*}
d(\psi|\theta) &= 2 E\_{\theta} \left[-\ln \frac{f(\mathbf{x} ; \psi) }{f(\mathbf{x} ; \theta) } \right] \\
&= \int -2 \ln \frac{f(\mathbf{x} ; \psi) }{f(\mathbf{x} ; \theta) } f(\mathbf{x};\theta) d\mathbf{x} \\
&= E\_{\theta}\left[ -2 \ln f(\mathbf{x} ; \psi) \right] - E\_{\theta}\left[ -2 \ln f(\mathbf{x};\theta)\right] \\
&= \Delta(\psi|\theta) - \Delta(\theta|\theta).
\end{align\*}

We want to pick the model that minimizes the first part (because the second part is free of $\psi$). AIC approximates that part as the sum of two things. The first part is the expectation of negative twice the log likelihood evaluated using the *estimated* parameters. You do not have access to this, but you can evaluate negative twice the likelihood with your estimates--so you have an unbiased estimator. The second part is an expectation that is approximated by a function of the dataset and the number of predictors; this is often called a penalty term. This is cool because we can use our data twice: once for estimating the parameters, and again for approximating the out of sample fit.

Personally, I can't guarantee that you don't need Normality. I suspect you don't, but every time I've looked into the details, I have used a Normal distribution to derive the formula.
After reading the resource pointed out by @Richard Hardy, my take-away is:

No, AIC does not necessarily assume that the residual distribution is normal. *However*, it *does* assume that the model was fit by maximum-likelihood rather than any other method (such as least-squares). If and only if the residuals of a least-squares fit are normal, the LS model is also the ML model, and AIC is meaningful.