It sounds right but I'm still dumbfounded as to why these particular games. I'd imagine games, of all sorts, could be categorized as "cause for negligence" with this rationale, no?
How do you come to that conclusion? As I recall, koans are from the Chinese, Japanese, etc., schools of (Mahayana) Buddhism -- specifically zen. But the linked article specifically states that these are from early texts (which would be more aligned to Theravada/pre-split).
It is a teaching. It actually tells you what to think, and how to get there.
He talks about negligence, not attending. And then he lists a bunch of games, the last of which is "imitating deformities". That example alone should get you thinking about misusing your purpose, about using the mind to escape and not be present. Inventing dragons to fight. All that.
I mean, it's all there, if you think about it for five minutes.
Am I missing something in my understanding of that list?