Thanks for posting a topic for this - it's always great to learn from others!
Personally, a lot of my better ideas come from improvising while studying a visual piece (such as in these game jams!), or experimenting with new plugins in a DAW. From there I try to find ways of fleshing those ideas out either with the harmony or counterpoint. I find this to be the tougher part of composing, especially if those other parts don't come organically during the improve itself. But in a way, I also find it rewarding to struggle with something to get the best parts that compliment each other and finally putting it all together.
What made composing for this game jam unique for me is that all of my ideas came from improvising on a keyboard, since I am primarily a guitar player :)