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

Answer: 
No, but the likelihood function used in the AIC formula should match the distribution of the residuals (see point 3. [here](http://robjhyndman.com/hyndsight/aic/)). If a normal likelihood is used when the residuals are actually non-normal, that will generally invalidate AIC (except perhaps for some special cases).
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.