Sure! Here's a simple game that meets all your requirements. The game will have a blue player that can be controlled from the four sides, and there will be a red enemy.
In this game, the blue player can be controlled using the arrow keys on a keyboard or by tapping/swiping on a smartphone screen. The player can move in all four directions (up, down, left, and right) within the game board (represented by the black border). The enemy (red square) is fixed at the top left corner.
Note: You can save the above code as an HTML file and open it in a web browser to play the game.