Yes, you need one. The game will stutter every second trying re-initializing XInput if you don't have a working controller plugged in. It is a problem that many console ports have. I recommend installing Special K. It can emulate the presence of a controller. The option is called XInput Placeholders. Special K can also help to run the game in borderless fullscreen mode.

I second that recommendation.

Special K is a useful tool for a lot of single-player games anyway, especially for folks whose computers aren't quite modern (and plenty of modern ones) - invaluable for some game like Nier Automata, The Tales series... I know I've used it to "fix" a lot of games, framerate, resolution, etc. Wonderful tool when it works.