Typical time series data like temperature, share market data etc, and even natural language sentences can be examples for sequence classification problems. Now in your case, if you're just talking about predicting rating, you should also think about predicting the next bought item. You could use an RNN to predict next item to be bought and also its rating. Please read more about RNNs.
With that said, if you don't want to use RNNs, you could as well convert the problem into regular classification problem as you have done and it should work.
In fact in regular (Not deep learning)NLP problems, they convert sequence problems to regular classification problems.