Sounds like an interesting challenge. But I don't know how to even start...

Like, how is it not a case of design a game, write an adventure for it, and then post it without the game rules? Seems like it's going to take just as much effort as just designing the game in the first place. I feel like I'm missing something.

Any hints? I don't suppose you have an example entry so I can understand what we're meant to be doing better?

Well, you could write an adventure and include stats, but not give any explanation of the stats. Or maybe build out a sourcebook that includes new resources and mechanics for the game, but declines to elaborate on the core mechanics of the game.

I think one thing that might be helpful is to think of a system not just as mechanics but also a theme, like space horror, black metal fantasy, or exploring dark and mysterious woods. So rather than thinking about the mechanics, make up a setting to put your entry in. I think your question is probably one a lot of people have, so maybe  the jam is a way to break the assumption that a system needs to be fully fleshed out or that you need a strong understanding of system mechanics to make ttrpg materials. This could also be a way for you to take the first step towards designing your own system without having to commit to writing a whole ass book. Doing research for this project I’ve found some people who do just that, they’ll make references to a game book before it’s come out but eventually they will publish it. I think the barrier to entry for writing a module is much lower than for designing a fully fledged system.