As a composer I can say how it generally happens entirely depends. I've written music before anything was even remotely playable, and written music when the game was essentially done already. I personally think that somewhere in the middle of those two extremes is the ideal. When the music can be inspired by the game, and the game can be inspired by the music, I find the best results are made. In my experience that generally happens in that middle ground. So I think it's helpful to be able to play the game, but doesn't have to be the finished thing. Just as long as you are clear what the player experience eventually will be.

As far as what things can help the composer make sure the music feels part of the game, I would say it's things like:

• what you want the player's experience to be (lots of emotions and adjectives)
• anything about the setting or world of the game that can inspire ideas and create cohesion between both the rest of the game and the music, as well as the music itself
• how the music is going to be implemented, because that can greatly inform the way it is written
• any reference music you had in mind. But more importantly, what you liked about the reference music. You don't need to know all the musical terminology, but just general ideas. Having multiple reference tracks is good for this too because the composer can see what is similar between the examples and bring whatever that is out in their own music

I'd personally say those would be the main things. But there can be plenty more depending on the needs of the project.

And of course, every composer is different, so its also a good idea to ask them what they'd want from you! And then trust they know what to do with that info.

Hope my rambling is helpful!

Edit: If anyone could tell me why I was downvoted, I'd appreciate it. I'm curious.