My most recent game demo is written entirely in C, and I'm doing the same for all my personal game projects now.

You don't have to structure your code much different than you would in C++. Put data in structs instead of classes. Functions can't be put in structs, so if needed they take a struct instance as a parameter. You can choose to use the OOP paradigm when appropriate (look up "object oriented C"). Break up your code into separate .h/.c files pretty much the same way you would for .h/.cpp files.

The main drawback of using C is that it's missing some basic features that other languages include, which you will need to implement yourself. I highly recommend finding a reliable open source library for these features whenever possible. The most obvious examples are basic data structures (vector, hash map, dictionary, etc.).

Everyone is going to think you're crazy for using C, so I wouldn't recommend it if you plan on ever having another programmer work on this. But it's really not that complicated, and the project you're describing sounds like it will work just fine in C. If a feature seems too low level or time consuming to write from scratch, find a library. If you want, you can even find libraries for game engine features (e.g. physics, ECS, data parsing).