The first two Powered Up train sets can be controlled with smart devices (phone, tablet, etc). Is this required to control the trains?
No, a smart device is not required to control train sets 60197 and 60198. These include a standalone Powered Up remote control:
This provides much of the same functionality as a smart device. From the FAQ:
The LEGO® Powered Up remote control works a lot like how you would use your smart device (mobile phone or tablet for example) to control any other electronic device via Bluetooth technology. If you connect the remote control to the Smarthub in the train, you can control the speed or stop the train.
However, there are some features that are only available from a smart device:
The app does provide you with additional features, such as sounds, and the ability to see how fast the train is travelling from 0-10 increments.