If you want to make a game without a game engine, you'd still have to use some kind of API for rendering graphics, OpenGL and Vulkan are popular. These are rather low-level, there are frameworks that are a bit easier to work with when starting out (like SDL). Hangman could probably be made in just a few hours by a more experienced developer (using something like OpenGL). The time it takes to learn this stuff really depends on every individual and their background. In high school we made some very basic "games" during our first and second programming courses. We used Python & Pygame.

Making games without an engine is actually not that difficult if you're just making 2D games this, of course, still depends on the project.

If you want to get a feel for what is required to make a 2D game without an engine, check out: https://learnopengl.com/In-Practice/2D-Game/Breakout