Games are required to be complete in order to be published under the HG label –
I could not find the vaguely remembered staff response I remember from the past but one of the requirements if I remember is that use of stats is mandatory in order for the game to be considered complete.
As @HarrisPS indicates, there is:
which has no stats, but I believe this is the exception that proves the rule. This was specifically written for the 2014 IF competition and as a result of being awarded 2nd place, I believe it was incorporated into the official CoG library.
Part of the real issue is the tension between authors/developers who view the end product of CSG (Choice Script Games) as books vs those who view them as actual games.
Any of the staff (or those with more tangible knowledge) can correct me but this has been my understanding of the issue.
Edit: @hustlertwo indicates that there is another, more recently published stat-less game in the HG library; so maybe, I am mis-remembering the staff response.
Edit 2: This thread is a good place to see a discussion about the use of stats in these games: