There are two or three reasons that I still have reservations about the 1927 or 1928 date for the introduction of Chinese Checkers.
First, I have a 1923 article about Mah Jongg which called the Mah Jongg pieces "chinese checkers". Mah Jongg was a popular game in the 1920's. Perhaps that is the game people were playing at the Chinese Checkers tournaments in 1927 into the early 1930's.
Second, which game pieces would Pressman have used in a 1928 version? Would they have been clay marbles? Wooden balls? There would be a limited selection of glass marbles available in 1927 or 1928.
Finally, the 1936 and later articles and advertisements call it a new game. The 1937 article with the picture considers it new enough that they need to explain the object of the game (and new enough to be worthy of a picture in the paper). And it's still being called new in 1938 in the Popular Science article how how to build your own gameboard.
That is why I suspect the earlier Chinese Checkers references might be about a different game, probably Mah Jongg.
Thank you for bumping this thread. It's a very interesting topic to me.