Was Knick knack an actual game?
Solution 1:
As suggested by the following source, knickknack may refer to tapping out a rhythm usin a spoon.
This traditional rhyme was first published in 1906 but almost certainly originates from earlier possibly from the time of the Irish potato famine.
The biggest clue to the meaning lies in the lyrics most particularly 'paddywhack' and to a lesser extent 'knick-knack'.
A knick-knack is a trinket or other trivial object. Knick-knack may also refer to the practice of tapping out a rhythm using spoons.
(www.learnarhyme.com)