Knowing nothing about his sales process and features, I would assume there are many complex non-linearities (to be possibly leveraged for better predictions). I find this statement bizarre.
But if you can give me an example of a non-linearity in sales forecasting that cannot be fit by a linear model but can by an RNN I'd honestly be really interested in that.
ARIMA models cannot take into consideration special scenarios or even multivariate features (Like location and time). It's good for simple forecasting but when you need more "human like" predictions we are betting on neural networks.
For example we would instinctively know that sales of turkey goes up on Thanksgiving. ARIMA model cannot factor this but RNN/LSTM should be able to (Theoretically speaking).
https://en.wikipedia.org/wiki/Dummy_variable_(statistics) https://en.wikipedia.org/wiki/Interaction_(statistics)
If you are convinced that there are complex non-linearities that an ARIMA model cannot describe, then I would try to use RNNs to find a pattern in your ARIMA models' residuals and try to augment your ARIMA model with an RNN.