Ex-game programmer and current PL programmer here. I think a better analogy is that you can make a game without having a scene graph. And, indeed, you can. And it works fine for many simple games, though as some scales it starts to be a hindrance.
But a fun fact, if you know about single-pass compiling, you can figure out a lot of why the original C syntax is what it is. A declaration is a "reserve some memory" statement. Local variables had to be declared at the beginning of scope so that the compiler could deallocate them at scope close. Without an AST, the compiler had to produce instructions immediately.
With a true AST, you don't need such a restrictive syntax.
There are many other possible examples.
But I think studying Lua [1] or the Wren codebase [2] is still worthwhile, provided you keep in mind that they're relatively simple languages that are designed to be both fast and embedded.
[1] https://www.lua.org/doc/jucs05.pdf [2] https://github.com/munificent/wren
PL (but not compiler) researcher here. What you're saying sounds to me like "One of the interesting insights I got while programming my own game was that despite what every game programming book says, there are games that can be programmed without defining any functions." I mean, yes, you can do that, and it may in fact be more efficient, but it's going to cause trouble down the line if you ever want to do something more complex.