There are a variety of game design contests out there. Each has its own requirements for entries. When it comes to these contests they generally don’t require the game to be done. But how close to done should it be? I can only answer definitively about The Board Game Workshop Design Contest.
For this contest the focus is unfinished games. I want games to enter that will benefit from the feedback and be able to improve.
To enter round one of the contest, you only need to be able to explain the idea of your game in the short description and 2-minute video. It’s not required that you have a fully developed game or even a prototype. That certainly doesn’t hurt though.
The more you put into your submission, the better your feedback will be. If you submit a very vague game idea, you will likely not score very well and judges won’t be able to give you useful feedback. The more you can show in your video, the more likely you are to get useful feedback.
To move onto round two, you will need to score highly in the five categories of innovation, elegance, excitement, presentation, and overall. But games at any stage are welcome and every entry will get feedback that will hopefully help it improve, whether or not it goes onto round two.