<<I think making instances (that is "separate occurances") is what has been done for these sentences I copied>>
I agree.
This is not official, but to me, where the object of "playing" is uncountable, then so is "playing." "I spent the afternoon playing checkers."
Where the object is countable, then so is "playing."
This is the fifth time he has played that damned record. I can't possibly sit through a sixth playing.
a playing of cards for money in an outhouse, would be an occurance, or an incidence of playing.
I find playing Chopin's nocturns on the piano to be very relaxing. Uncountable.
On each playing of the fifth nocturn, I improve very slightly. Countable.
While Chopin's nocturns are clearly countable, the playing of them in general is not. It's like eating potato chips. The chips are countable but the eating of them in general is not. But you could refer to a particular occasion on which you ate too many as
an excessive eating of potato chips. This would be opposed to "
the excessive eating of potato chips," which would be habitual.
At universities where the dining room cannot accomodate the entire student body, they sometimes have what is called "a second sitting."
Best wishes, - A.