The question isn't asking for a list of games, it's asking if a type of game exists at all. An answer could exist that is clear, concrete, and well-defined.
Does the category exist?
Here are some similar questions, asking if a category exists at all. I think these are not asking for lists:
A single piece of evidence that the category exists would be sufficient to answer the question; showing that the category doesn't exist would do likewise. Once answered in such a way, additional proofs would provide no benefit.
And that's what Stack Exchange is really about -- getting a single, clear response that decisively answers the question.
List everything in the category.
These, however, are similar, but are just asking for lists:
- Who has been to the top of Mt. Everest?
- What biographies were written of Churchill while he was alive?
- What numbers are prime?
- Which board games were invented before 1900?
A single piece of evidence wouldn't fully answer these questions. In fact, a complete answer would have to enumerate all members of the category. Each answer that adds another member to the list would only be a small piece of the true answer to the question.
And that's what Stack Exchange isn't about -- gradually piecing together a complete response through reading many, many answers to a question.
What I think we should decide.
I suggest we refine the concept of "recommendation questions". Questions that can be fully answered by mentioning a single game should be on topic.
Consider that we already accept questions like:
- What's that game where you throw colored sticks on the table?
This is very similar to asking:
- Is there a category of games where you throw colored sticks on the table?
In that vein, I suggest we allow category-existence questions under the same rules we should use for game-identification questions.
- The attribute of the thing being sought must be clearly described. We wouldn't want game-identification questions like "What's that one with the cards or something?", just like we wouldn't want category-existence questions like "Are there any games with cards or something?".
- A good category-existence/game-identification question delineates a small set. If someone asks for help identifying a game that they played in 1990 that used dice and cards and a board, the description is clear, but it describes too large a set. Likewise, if someone asks if games ever use dice, it's such a common feature that it's a poor category-existence question. Asking if there were any Navajo-language games published in 1990 is a much smaller set.
- Most importantly, the correct answer only needs to mention a single game. A good game-identification question is fully answerable with a single game -- the one they're looking for. A good category-existence question is fully answerable with a single game -- a member of that category. A poor question (of either of these types) couldn't be answered without a list.