No, you don't strictly need a game engine to make a game. However, using a game engine can greatly simplify the process and allow you to focus more on the gameplay, art, and story.
Without a game engine, you would need to write all of the code yourself from scratch for everything including rendering, physics, audio, and more. This is not only a lot of work, but also requires a broad range of expertise in various complex fields such as 3D graphics and physics simulation.
If you decide to develop a game without an engine, here's a simple example of how you might create a window and render a basic 2D shape using OpenGL in C++:
On the other hand, if you use a game engine like Unity or Unreal, many of these features are provided out of the box. For example, in Unity, creating a sprite on the screen could be as simple as dragging and dropping an image into your scene in the editor.
The choice between using a game engine or not depends largely on your game's requirements, your team's skill set, and the resources you have available. However, for most game developers—particularly those just starting out—a game engine is an invaluable tool that can save a lot of time and effort.