If "winning" the beer game means not overreacting to short-term signals, then you can view that as a form of slack. You're sometimes paying a bit extra to hold onto something that you have no immediate short-term use for.
I'm not sure it's the same kind of buffering. I would assume the "winning" strategy for the case when the known final demand is fixed is to maintain fixed the upstream orders, and buffer outcome, and for non-fixed final demand is to model that demand as good as possible and keep upstream orders accordingly to maintain outcome matching the demand model. Large penalties for buffering may make this approach not working, I guess...
Proportional-only buffer management makes the bullwhip effect worse.
You need an integral part that knows what the entire chain reaction time is. But if you don't have a buffer, you can't do that part, you can only react strictly to the conditions your suppliers have right now.
A derivative part seems quite useless in a non-coordinated game. But it could in theory pass a "message" upchain that they need to start reacting. Anyway in any real situation it will be easier to pass a message around by telling stuff to people.
At the end of the day, the relative penalty for storage or non-delivery is what will dictate the optimum play style. But it's perfectly viable to use buffers to attenuate the bullwhip instead of making it larger.