[0] https://blog.demofox.org/2015/02/08/estimating-set-membershi...
[0] https://blog.demofox.org/2015/02/08/estimating-set-membershi...
With that in mind, bloomfilters should be used for things where you are only interested to know if it is not in the set, or when you can tolerate a given false positive rate and size it accordingly.
For the first example will give false positives and be hostile to players that have not attacked. That might be okay, but not what you expect, and you might as well use probability for that. The second example I suppose you can use it to only try things you haven't tried before, but it seems weird.
That said, the link you provided is actually a good post about the topic, and include some good insight. It's not trying to hide that bloom filters are No or Maybe.
In the chess example, knowing it's possible to lose from X positions is almost meaningless most of the time. The issue is search space sizes are either to large to be useful or small enough for brute force.
In the chess example the most importan thing its not for the machine to win (or lose); is so the user feels its not the same game they already played; or -dare I say- think that the enemy is "learning"
Even ignoring that and assuming you wanted to do a lookup vs all games played with someone that's a tiny dataset so looking it up has no real downside.