Evan after the United States Board on Geographic Names changed the city's name to "Pittsburg" you could still find the use of "Pittsburgh" in many places such as the pin and World Series panoramic found below.
But my potential theory is that despite the fact that the city's name was changed, the registered name of the ball club itself never changed, and the club in those days was technically called the "Pittsburgh Baseball Club" operated or owned by the "Pittsburgh Athletic Company" as you can see from the 1908 Honus Wagner contract also pictured below. So perhaps this is why it was spelled with the "h" on the Tip Tops?
But it is also interesting to note that on the contract, the city is spelled with the "h" as well at the top. So even a legal document being signed in 1908 was spelled with the "h".
