No, there is no problem in the game, just press the buttons, it is because there is no animation. I would be happy if you play it again and re-evaluate. Also, look at the video on the itch page, the character is walking.
ooooh... ok nice ! i like it but maybe you should just put a green plant or a tree or something visible from the beginning so it makes it obvious you are indeed walking. beside that it's nice !