Google Play does not have a definition of what counts as a “Complete game”. So yes, you are allowed to submit an unfinished project. However keep the following in mind:
- Google Play has support for Alpha and Beta versions of an app. These might work in your case, as users will have the expectations that the project is not finished yet, although I’m not sure how it affects visibility.
- Make sure you are perfectly clear to potential customers what your app does and does not include. The last thing you want is negative reviews from people expecting a full game, before it is fully released.
- As you noted yourself, you need to charge from the very beginning.
I’ve used Google Play a lot a year or two ago, not sure how much things have changed since then, but I’m fairly positive it’s still (roughly) the same.