Interesting thought. Obvously, it depends on the jam's rules.

But do people in general understand "no ai generated content" to include the code?

At first glance, one might think, yes, of course, that code is ai generated, how can you even doubt that it should not be included.

But how does coding with help of ai actually look? If it is writing in a high level language (like english), so the computer does what you want it to do, than, no, that might be called ai coding, but it is not. It is exactly what I just said. Using a high level language. Instead of coding in assembler, you use a compiler to use human understandable words. And instead of doing everything yourself you rely on the works of others that did it before and include their work with a library. The use of ai ist just a compiler that translates your language into a "lower" language , that in turn can get translated to machine code. And that "ai compiler" also uses a "library of previoius works" to do so.

Using a game engine is similar, in that you do not have to do the actual coding yourself very much.

Of course, if there is a jam with a theme of "doing it by hand" they should specify which tools are not allowed. After all, there were computer games before the spread of engines like Unity, Godot and all those here https://itch.io/game-development/engines

For art (read: images), the best analogy I came up with so far, is canvas painters and photographers. The photographers do not create the image the same way painters would. They chose the motive, they operate technical tools, they have influence over the composition and ultimatly do very many pics and select the best ones. And they cheat with makeup, lighting and in recent decades with digital enhancements.

But for computer code, using ai generated code is just a continuation of the language models, a higher level of abstraction, making pseudo code the actual code.