Does one need a controller to play this game, or can I play it with mouse and keyboard?

A controller is not required to play, mouse and keyboard is adequate.
The default keybinds are all mapped to the keyboard, and can all be rebound within the game. The majority of the gameplay constitutes movement and a confirmation/cancellation only, with a few keys extra for menus, meaning that I could play most of the game with one hand if I rebound the keys to my liking.